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1.
In this paper we study nonlinear second-order differential inclusions involving the ordinary vectorp-Laplacian, a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general
and unifying and incorporates gradient systems, evolutionary variational inequalities and the classical boundary value problems,
namely the Dirichlet, the Neumann and the periodic problems. Using notions and techniques from the nonlinear operator theory
and from multivalued analysis, we obtain solutions for both the ‘convex’ and ‘nonconvex’ problems. Finally, we present the
cases of special interest, which fit into our framework, illustrating the generality of our results. 相似文献
2.
In this paper a technique is developed for the study of the existence and uniqueness of solutions to nth order ordinary differential equations satisfying n-point boundary conditions. Liapunov-like functions are employed to determine the existence and uniqueness of solutions to linear equations satisfying the boundary conditions, and these solutions are in turn used to determine existence for the general nonlinear case. A by-product of this technique is a matching technique for linear equations by which solutions of certain k-point boundary value problems (k < n) can be matched to extend the interval of existence for solutions to the n-point problem. 相似文献
3.
Francisco Periago 《Journal of Mathematical Analysis and Applications》2003,280(2):413-423
In this paper, we consider the semilinear initial value problem associated with an operator A whose spectrum lies in a sector of the complex plane and whose resolvent satisfies (z−A)−1M|z|γ for some −1<γ<0 and all z outside the sector. The properties of existence and uniqueness of global mild solutions and continuous dependence on the initial data are investigated. 相似文献
4.
Nicholas Fewster-Young Christopher C. Tisdell 《Nonlinear Analysis: Theory, Methods & Applications》2012
This article analyzes qualitative properties of solutions to two-point boundary value problems for singular ordinary differential equations. In particular, we form new approaches that ensure that all possible solutions satisfy certain a priori bounds. The methods involve differential inequalities. 相似文献
5.
James A. Pennline 《Journal of Mathematical Analysis and Applications》1983,96(2):584-598
Constructive existence and uniqueness theorems are presented for the problem . Applications to several problems are also given including one in which the boundary values are y′(0) = y′0, y(1) = y1. 相似文献
6.
7.
Marian Kwapisz 《Applicable analysis》2013,92(1-4):169-182
Existence and uniqueness results for bvp problems for difference equations are discussed. The weighted norm technique and the Banach contraction mapping principle are employed 相似文献
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10.
S. A. Brykalov 《Differential Equations》2014,50(2):169-176
We obtain sufficient conditions for the existence of at least one absolutely continuous solution of a nonlinear functional-differential inclusion in a finite-dimensional space with nonlinear set-valued functional boundary conditions. The set-valuedness of the dynamics may be due to the presence of a control. In addition, we consider the case in which the set-valuedness of the system dynamics and the boundary conditions is specified by inequalities. We assume the presence of a continuous feedback and impose the requirements of solvability of the open-loop problem. Statements of problems of this type arise in connection with the analysis of conflict-control systems. 相似文献
11.
《Journal of Computational and Applied Mathematics》2006,193(1):269-276
Here we are concerned with the existence of positive solution for autonomous and nonautonomous second-order systems with multi-points boundary conditions. For nonautonomous systems we use the Schauder's fixed point theorem in a suitable Banach space, while for autonomous ones using fixed point theorems is usually useless because of the existence of trivial solution and for this we employed a method based on the implicit function theorem and topological degree. In order to verify the obtained results, we have considered some definite systems to verify the results numerically. 相似文献
12.
In this paper, we consider the nonlinear discrete boundary value problem
13.
In this paper we consider two quasilinear boundary value problems. The first is vector valued and has periodic boundary conditions.
The second is scalar valued with nonlinear boundary conditions determined by multivalued maximal monotone maps. Using the
theory of maximal monotone operators for reflexive Banach spaces and the Leray-Schauder principle we establish the existence
of solutions for both problems. 相似文献
14.
We prove local existence, uniqueness, Hölder regularity in space and time, and smooth dependence in Hölder spaces for a general class of quasilinear parabolic initial boundary value problems with nonsmooth data. As a result the gap between low smoothness of the data, which is typical for many applications, and high smoothness of the solutions, which is necessary for the applicability of differential calculus to abstract formulations of the initial boundary value problems, has been closed. The theory works for any space dimension, and the nonlinearities in the equations as well as in the boundary conditions are allowed to be nonlocal and to have any growth. The main tools are new maximal regularity results (Griepentrog in Adv Differ Equ 12:781–840, 1031–1078, 2007) in Sobolev–Morrey spaces for linear parabolic initial boundary value problems with nonsmooth data, linearization techniques and the Implicit Function Theorem. 相似文献
15.
James M. Hill 《Acta Appl Math》1990,18(2):195-197
Book Review
Boundary value problems of finite elasticity, local theorems on existence, uniqueness, and analytic dependence on dataTullio Valent: Springer Tracts in Natural Philosophy, Volume 31 (Edited by C. Truedell), Springer, New York, 1988, xii + 192 pp 相似文献16.
About uniqueness for nonlinear boundary value problems 总被引:3,自引:0,他引:3
V. Schuchman 《Mathematische Annalen》1984,267(4):537-542
17.
We use the methods of microlocal analysis to give a new proof of a theorem of Kohn and Vogelius, showing that the boundary values of a continuous isotropic conductivity can be recovered from voltage and current measurements at the boundary. Moreover, we prove sharp estimates to establish the continuous dependence of the boundary values of the conductivity on the voltage to current maps. 相似文献
18.
Zi-Cai Li Qing Fang Hung-Tsai Huang Yimin Wei 《Journal of Computational and Applied Mathematics》2009,233(2):293-307
In this paper, we consider the problem of solution uniqueness for the second order elliptic boundary value problem, by looking at its finite element or finite difference approximations. We derive several equivalent conditions, which are simpler and easier than the boundedness of the entries of the inverse matrix given in Yamamoto et al., [T. Yamamoto, S. Oishi, Q. Fang, Discretization principles for linear two-point boundary value problems, II, Numer. Funct. Anal. Optim. 29 (2008) 213–224]. The numerical experiments are provided to support the analysis made. Strictly speaking, the uniqueness of solution is equivalent to the existence of nonzero eigenvalues in the corresponding eigenvalue problem, and this condition should be checked by solving the corresponding eigenvalue problems. An application of the equivalent conditions is that we may discover the uniqueness simultaneously, while seeking the approximate solutions of elliptic boundary equations. 相似文献
19.
Stephen Clark Johnny Henderson 《Proceedings of the American Mathematical Society》2006,134(11):3363-3372
For the third order differential equation, we consider uniqueness implies existence results for solutions satisfying the nonlocal -point boundary conditions, Uniqueness of solutions of such boundary value problems is intimately related to solutions of the third order equation satisfying certain nonlocal -point boundary conditions. These relationships are investigated as well.
20.
Abdelkader Boucherif 《Journal of Mathematical Analysis and Applications》1980,77(2):577-600
In the present work, we investigate nonlinear three-point boundary value problems (second-order differential equations with boundary conditions imposed at three consecutive points) in an effort to understand the conditions that must be imposed upon nonlinear perturbations of a linear problem in order to obtain a solution of a three-point problem. Both the noncritical case and the critical case are considered. In the first case, existence and uniqueness results are obtained, and in the second case we deal with local bifurcation problems when the nonlinearities are quadratic and cubic. 相似文献