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1.
In this paper, we study a Neumann problem for elliptic systems with variable exponents. We obtain the existence of at least
three nontrivial solutions by using an equivalent variational approach to a recent Ricceri’s three critical points theorem
(Ricceri in Nonlinear Anal TMA 70:3084–3089, 2009). 相似文献
2.
Nguyen Thi Quynh Trang 《Optimization Letters》2012,6(4):749-762
In this paper we investigate the Lipschitz-like property of the solution mapping of parametric variational inequalities over
perturbed polyhedral convex sets. By establishing some lower and upper estimates for the coderivatives of the solution mapping,
among other things, we prove that the solution mapping could not be Lipschitz-like around points where the positive linear
independence condition is invalid. Our analysis is based heavily on the Mordukhovich criterion (Mordukhovich in Variational
Analysis and Generalized Differentiation. vol. I: Basic Theory, vol. II: Applications. Springer, Berlin, 2006) of the Lipschitz-like property for set-valued mappings between Banach spaces and recent advances in variational analysis.
The obtained result complements the corresponding ones of Nam (Nonlinear Anal 73:2271–2282, 2010) and Qui (Nonlinear Anal 74:1674–1689, 2011). 相似文献
3.
Recently, O’Hara, Pillay and Xu (Nonlinear Anal. 54, 1417–1426, 2003) considered an iterative approach to finding a nearest common fixed point of infinitely many nonexpansive mappings in a Hilbert
space. Very recently, Takahashi and Takahashi (J. Math. Anal. Appl. 331, 506–515, 2007) introduced an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions
of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. In this paper, motivated
by these authors’ iterative schemes, we introduce a new iterative approach to finding a common element of the set of solutions
of an equilibrium problem and the set of common fixed points of infinitely many nonexpansive mappings in a Hilbert space.
The main result of this work is a strong convergence theorem which improves and extends results from the above mentioned papers. 相似文献
4.
In this paper, we establish a decay result of global solutions and the existence of the global attractor for higher-dimensional
linear thermoviscoelastic equations by introducing a velocity feedback on a part of the boundary and using multiplier techniques.
We extend the results in Messaoudi and Mustafa (Nonlinear Anal. TMA 10:3132–3140, 2009) for a viscoelastic system to those for a thermoviscoelastic system. 相似文献
5.
We introduce a new iterative method in order to approximate a locally unique solution of variational inclusions in Banach
spaces. The method uses only divided differences operators of order one. An existence–convergence theorem and a radius of
convergence are given under some conditions on divided difference operator and Lipschitz-like continuity property of set-valued
mappings. Our method extends the recent work related to the resolution of nonlinear equation in Argyros (J Math Anal Appl
332:97–108, 2007) and has the following advantages: faster convergence to the solution than all the previous known ones in Argyros and Hilout
(Appl Math Comput, 2008 in press), Hilout (J Math Anal Appl 339:53–761, 2008, Positivity 10:673–700, 2006), and we do not need to evaluate any Fréchet derivative. We provide also an improvement of the ratio of our algorithm under
some center-conditions and less computational cost. Numerical examples are also provided.
相似文献
6.
In this paper, we introduce an iterative method for finding a common element of the set of fixed points of a nonexpansive
mapping and the set of common fixed points of a countable family of nonexpansive mappings in Hilbert spaces. Using the result
we consider a strong convergence theorem in variational inequalities and equilibrium problems. The result present in this
paper extend and improve the corresponding result of Qin et al. (Nonlinear Anal 69:3897–3909, 2008), Plubtieng and Punpaeng
(J Math Anal Appl 336:455–469, 2007) and many others. 相似文献
7.
Rufus Willett 《Integral Equations and Operator Theory》2011,69(3):301-316
We provide a proof of an index theorem for band-dominated operators with slowly oscillating coefficients. The statement is
essentially the same as the main result of the announcement of Deundyak and Shteinberg (Funct Anal Appl 19(4):321–323, 1985), but our methods are very different from those hinted at there. The index theorem we prove can also be seen as a partial
generalization to higher dimensions of the main result of the article of Rabinovich et al. (Integr Equ Oper Theory 49:221–238,
2004). 相似文献
8.
Ram U. Verma 《Journal of Optimization Theory and Applications》2012,155(1):196-214
Based on the generalized graph convergence, first a general framework for an implicit algorithm involving a sequence of generalized resolvents (or generalized resolvent operators) of set-valued A-maximal monotone (also referred to as A-maximal (m)-relaxed monotone, and A-monotone) mappings, and H-maximal monotone mappings is developed, and then the convergence analysis to the context of solving a general class of nonlinear implicit variational inclusion problems in a Hilbert space setting is examined. The obtained results generalize the work of Huang, Fang and Cho (in J. Nonlinear Convex Anal. 4:301–308, 2003) involving the classical resolvents to the case of the generalized resolvents based on A-maximal monotone (and H-maximal monotone) mappings, while the work of Huang, Fang and Cho (in J. Nonlinear Convex Anal. 4:301–308, 2003) added a new dimension to the classical resolvent technique based on the graph convergence introduced by Attouch (in Variational Convergence for Functions and Operators, Applied Mathematics Series, Pitman, London 1984). In general, the notion of the graph convergence has potential applications to several other fields, including models of phenomena with rapidly oscillating states as well as to probability theory, especially to the convergence of distribution functions on ℜ. The obtained results not only generalize the existing results in literature, but also provide a certain new approach to proofs in the sense that our approach starts in a standard manner and then differs significantly to achieving a linear convergence in a smooth manner. 相似文献
9.
In this paper, we introduce two iterative schemes (one implicit and one explicit) for finding a common element of the set
of solutions of the generalized equilibrium problems and the set of all common fixed points of a nonexpansive semigroup in
the framework of a real Hilbert space. We prove that both approaches converge strongly to a common element of such two sets.
Such common element is the unique solution of a variational inequality, which is the optimality condition for a minimization
problem. Furthermore, we utilize the main results to obtain two mean ergodic theorems for nonexpansive mappings in a Hilbert
space. The results of this paper extend and improve the results of Li et al. (J Nonlinear Anal 70:3065–3071, 2009), Cianciaruso et al. (J Optim Theory Appl 146:491–509, 2010) and many others. 相似文献
10.
Belkacem Said-Houari Salim. A. Messaoudi Aissa Guesmia 《NoDEA : Nonlinear Differential Equations and Applications》2011,18(6):659-684
This work is concerned with a system of two viscoelastic wave equations with nonlinear damping and source terms acting in
both equations. Under some restrictions on the nonlinearity of the damping and the source terms, we prove that, for certain
class of relaxation functions and for some restrictions on the initial data, the rate of decay of the total energy depends
on those of the relaxation functions. This result improves many results in the literature, such as the ones in Messaoudi and
Tatar (Appl. Anal. 87(3):247–263, 2008) and Liu (Nonlinear Anal. 71:2257–2267, 2009) in which only the exponential and polynomial decay rates are considered. 相似文献
11.
Stability Analysis for Minty Mixed Variational Inequality in Reflexive Banach Spaces 总被引:1,自引:0,他引:1
This paper is devoted to the stability analysis for a class of Minty mixed variational inequalities in reflexive Banach spaces,
when both the mapping and the constraint set are perturbed. Several equivalent characterizations are given for the Minty mixed
variational inequality to have nonempty and bounded solution set. A stability result is presented for the Minty mixed variational
inequality with Φ-pseudomonotone mapping in reflexive Banach space, when both the mapping and the constraint set are perturbed
by different parameters. As an application, a stability result for a generalized mixed variational inequality is also obtained.
The results presented in this paper generalize and extend some known results in Fan and Zhong (Nonlinear Anal., Theory Methods
Appl. 69:2566–2574, 2008) and He (J. Math. Anal. Appl. 330:352–363, 2007). 相似文献
12.
The purpose of this paper is to consider a shrinking projection method of finding the common element of the set of common
fixed points for a finite family of a ξ-strict pseudo-contraction, the set of solutions of a systems of equilibrium problems
and the set of solutions of variational inclusions. Then, we prove strong convergence theorems of the iterative sequence generated
by the shrinking projection method under some suitable conditions in a real Hilbert space. Our results improve and extend
recent results announced by Peng, Wang, Shyu and Yao (J Inequal Appl, 2008:15, Article ID 720371, 2008), Takahashi, Takeuchi and Kubota (J Math Anal Appl 341:276–286, 2008), Takahashi and Takahashi (Nonlinear Anal 69:1025–1033, 2008) and many others. 相似文献
13.
We introduce the new idea of recurrent functions to provide a new semilocal convergence analysis for Newton-type methods,
under mild differentiability conditions. It turns out that our sufficient convergence conditions are weaker, and the error
bounds are tighter than in earlier studies in some interesting cases (Chen, Ann Inst Stat Math 42:387–401, 1990; Chen, Numer Funct Anal Optim 10:37–48, 1989; Cianciaruso, Numer Funct Anal Optim 24:713–723, 2003; Cianciaruso, Nonlinear Funct Anal Appl 2009; Dennis 1971; Deuflhard 2004; Deuflhard, SIAM J Numer Anal 16:1–10, 1979; Gutiérrez, J Comput Appl Math 79:131–145, 1997; Hernández, J Optim Theory Appl 109:631–648, 2001; Hernández, J Comput Appl Math 115:245–254, 2000; Huang, J Comput Appl Math 47:211–217, 1993; Kantorovich 1982; Miel, Numer Math 33:391–396, 1979; Miel, Math Comput 34:185–202, 1980; Moret, Computing 33:65–73, 1984; Potra, Libertas Mathematica 5:71–84, 1985; Rheinboldt, SIAM J Numer Anal 5:42–63, 1968; Yamamoto, Numer Math 51: 545–557, 1987; Zabrejko, Numer Funct Anal Optim 9:671–684, 1987; Zinc̆ko 1963). Applications and numerical examples, involving a nonlinear integral equation of Chandrasekhar-type, and a differential
equation are also provided in this study. 相似文献
14.
In this paper, we study a variation of the equations of a chemotaxis kinetic model and investigate it in one dimension. In
fact, we use fractional diffusion for the chemoattractant in the Othmar–Dunbar–Alt system (Othmer in J Math Biol 26(3):263–298,
1988). This version was exhibited in Calvez in Amer Math Soc, pp 45–62, 2007 for the macroscopic well-known Keller–Segel model in all space dimensions. These two macroscopic and kinetic models are related
as mentioned in Bournaveas, Ann Inst H Poincaré Anal Non Linéaire, 26(5):1871–1895, 2009, Chalub, Math Models Methods Appl Sci, 16(7 suppl):1173–1197, 2006, Chalub, Monatsh Math, 142(1–2):123–141, 2004, Chalub, Port Math (NS), 63(2):227–250, 2006. The model we study here behaves in a similar way to the original model in two dimensions with the spherical symmetry assumption
on the initial data which is described in Bournaveas, Ann Inst H Poincaré Anal Non Linéaire, 26(5):1871–1895, 2009. We prove the existence and uniqueness of solutions for this model, as well as a convergence result for a family of numerical
schemes. The advantage of this model is that numerical simulations can be easily done especially to track the blow-up phenomenon. 相似文献
15.
In this paper, we study the solution stability of parametric weak Vector Variational Inequalities with set-valued and single-valued
mappings, respectively. We obtain the lower semicontinuity of the solution mapping for the parametric set-valued weak Vector
Variational Inequality with strictly C-pseudomapping in reflexive Banach spaces. Moreover, under some requirements that the mapping satisfies the degree conditions,
we establish the lower semicontinuity of the solution mapping for a parametric single-valued weak Vector Variational Inequality
in reflexive Banach spaces, by using the degree-theoretic approach. The results presented in this paper improve and extend
some known results due to Kien and Yao (Set-Valued Anal. 16:399–412, 2008) and Wong (J. Glob. Optim. 46:435–446, 2010). 相似文献
16.
We introduce an iterative sequence for finding the solution to 0∈T(v), where T
:
E⇉E
* is a maximal monotone operator in a smooth and uniformly convex Banach space E. This iterative procedure is a combination of iterative algorithms proposed by Kohsaka and Takahashi (Abstr. Appl. Anal.
3:239–249, 2004) and Kamamura, Kohsaka and Takahashi (Set-Valued Anal. 12:417–429, 2004). We prove a strong convergence theorem and a weak convergence theorem under different conditions respectively and give an
estimate of the convergence rate of the algorithm. An application to minimization problems is given.
This work was partially supported by the National Natural Sciences Grant 10671050 and the Heilongjiang Province Natural Sciences
Grant A200607. The authors thank the referees for useful comments improving the presentation and Professor K. Kohsaka for
pointing out Ref. 7. 相似文献
17.
We mainly investigate some properties of quasiconformal mappings between smooth 2-dimensional surfaces with boundary in the
Euclidean space, satisfying certain partial differential equations (inequalities) concerning Laplacian, and in particular
satisfying Laplace equation and show that these mappings are Lipschitz. Conformal parametrization of such surfaces and the
method developed in our paper (Kalaj and Mateljević, J Anal Math 100:117–132, 2006) have important role in this paper. 相似文献
18.
Applying generalized KKM-type theorems established in our previous paper (Khanh et al. in Nonlinear Anal. 71:1227–1234, 2009), we prove the existence of solutions to a general variational inclusion problem, which contains most of the existing results
of this type. As applications, we obtain minimax theorems in various settings and saddle-point theorems in particular. Examples
are given to explain advantages of our results. 相似文献
19.
Ioannis K. Argyros 《Numerical Algorithms》2010,54(4):485-501
We provide a semilocal convergence analysis for a certain class of secant-like methods considered also in Argyros (J Math
Anal Appl 298:374–397, 2004, 2007), Potra (Libertas Mathematica 5:71–84, 1985), in order to approximate a locally unique solution of an equation in a Banach space. Using a combination of Lipschitz and
center-Lipschitz conditions for the computation of the upper bounds on the inverses of the linear operators involved, instead
of only Lipschitz conditions (Potra, Libertas Mathematica 5:71–84, 1985), we provide an analysis with the following advantages over the work in Potra (Libertas Mathematica 5:71–84, 1985) which improved the works in Bosarge and Falb (J Optim Theory Appl 4:156–166, 1969, Numer Math 14:264–286, 1970), Dennis (SIAM J Numer Anal 6(3):493–507, 1969, 1971), Kornstaedt (1975), Larsonen (Ann Acad Sci Fenn, A 450:1–10, 1969), Potra (L’Analyse Numérique et la Théorie de l’Approximation 8(2):203–214, 1979, Aplikace Mathematiky 26:111–120, 1981, 1982, Libertas Mathematica 5:71–84, 1985), Potra and Pták (Math Scand 46:236–250, 1980, Numer Func Anal Optim 2(1):107–120, 1980), Schmidt (Period Math Hung 9(3):241–247, 1978), Schmidt and Schwetlick (Computing 3:215–226, 1968), Traub (1964), Wolfe (Numer Math 31:153–174, 1978): larger convergence domain; weaker sufficient convergence conditions, finer error bounds on the distances involved, and
a more precise information on the location of the solution. Numerical examples further validating the results are also provided. 相似文献
20.
L. C. Ceng S. Schaible J. C. Yao 《Journal of Optimization Theory and Applications》2008,139(2):403-418
We introduce an implicit iteration scheme with a perturbed mapping for finding a common element of the set of solutions of
an equilibrium problem and the set of common fixed points of finitely many nonexpansive mappings in a Hilbert space. Then,
we establish some convergence theorems for this implicit iteration scheme which are connected with results by Xu and Ori (Numer.
Funct. Analysis Optim. 22:767–772, 2001), Zeng and Yao (Nonlinear Analysis, Theory, Methods Appl. 64:2507–2515, 2006) and Takahashi and Takahashi (J. Math. Analysis Appl. 331:506–515, 2007). In particular, necessary and sufficient conditions for strong convergence of this implicit iteration scheme are obtained.
In this research, the first author was partially supported by the National Science Foundation China (10771141), Ph.D. Program
Foundation of Ministry of Education of China (20070270004), and Science and Technology Commision of Shanghai Municipality
Grant (075105118). 相似文献