共查询到20条相似文献,搜索用时 15 毫秒
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Maisa Khader 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(12):3945-3963
We study the long time behavior of solutions for damped wave equations with absorption. These equations are generally accepted as models of wave propagation in heterogeneous media with space-time dependent friction a(t,x)ut and nonlinear absorption |u|p−1u (Ikawa (2000) [17]). We consider 1<p<(n+2)/(n−2) and separable a(t,x)=λ(x)η(t) with λ(x)∼(1+|x|)−α and η(t)∼(1+t)−β satisfying conditions (A1) or (A2) which are given. The main results are precise decay estimates for the energy, L2 and Lp+1 norms of solutions. We also observe the following behavior: if α∈[0,1), β∈(−1,1) and 0<α+β<1, there are three different regions for the decay of solutions depending on p; if α∈(−∞,0) and β∈(−1,1), there are only two different regions for the decay of the solutions depending on p. 相似文献
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The paper encompasses a complete study of the weak-star extensibility of subspaces of Banach spaces introduced by B.S. Mordukhovich and B. Wang when studying the restrictive metric regularity in variational analysis. Many useful properties are presented; in particular, a new point of view and formulation of the property in the framework of Banach space theory is established. We also propose the concept of weak-star extensible Banach spaces that has interesting applications, and is fairly broad in that it contains many important classes of Banach spaces. Some further applications of this extensibility to the theory of linear operators between Banach spaces are also explored. 相似文献
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Lixin Tian Yuexia ChenYue Liu Ying Gao 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(8):2802-2812
This paper studies low-regularity solutions of the periodic general Degasperis-Procesi equation with an initial value. The existence and the uniqueness of solutions are proved. The results are illustrated by considering the periodic peakons of the periodic general Degasperis-Procesi equation. 相似文献
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We are concerned with an inverse problem for a degenerate linear evolution equation of first-order. Both hyperbolic and parabolic cases will be considered. We indicate sufficient conditions for the existence and uniqueness of a solution. All the results can be applied to inverse problems for equations from mathematical physics. As a possible application of the abstract theorems, some examples of partial differential equations are given. 相似文献
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The existence of catΩ(Ω) positive solutions for the p-Laplacian system with convex and Sobolev critical nonlinearities is obtained by some standard variational methods, whose key is to construct homotopies between Ω and levels of the functional Jλ,μ, and some analytical techniques. 相似文献
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Pham Huu Sach Nguyen Ba Minh 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(11):3994-4004
In this paper, we introduce new versions of ?-dual problems of a vector quasi-equilibrium problem with set-valued maps, and we give an ?-duality result between approximate solutions of the primal and dual problems. As the first application of the main result, we obtain an ?-duality for a vector quasi-equilibrium problem whose ?-solutions are understood in the sense of proper efficiency. The second application is devoted to an?-duality for a vector optimization problem with set-valued maps. 相似文献
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Felix Sadyrbaev Inara Yermachenko 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(12):e176
A quasi-linear boundary value problem has a solution with properties induced by oscillatory properties of the linear part of an equation. This result is proved for two dimensional systems. Consequences for Φ-Laplacian equations and problems with resonant linear parts are discussed. 相似文献
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This paper introduces an iteration scheme for viscosity approximation of a zero of accretive operator in a reflexive Banach space with weakly continuous duality mapping. A new iterative sequence is introduced and strong convergence of the algorithm {xn} is proved. The results improve and extend the results of Su [Xiaolong Qin, Yongfu Su, Approximation of a zero point of accretive operator in Banach spaces, J. Math. Anal. Appl. 320 (2007) 415-424] and some others. 相似文献
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Sehie Park 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(2):549-554
All results in “Some properties of abstract convexity structures on topological spaces” by S.-w. Xiang and H. Yang [S.-w. Xiang, H. Yang, Some properties of abstract convexity structures on topological spaces, Nonlinear Analysis 67 (2007) 803-808] and “A further characteristic of abstract convexity structures on topological spaces” by S.-w. Xiang and S. Xia [S.-w. Xiang, S. Xia, A further characteristic of abstract convexity structures on topological spaces, J. Math. Anal. Appl. 335 (2007) 716-723] are shown to be consequences of known ones or can be stated in more general forms. 相似文献
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Ravi P. Agarwal Claudio Cuevas Herme Soto 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(5):1769-1798
This work deals with the existence and uniqueness of pseudo-almost periodic and asymptotically ω-periodic mild solutions to some evolution equations in Banach spaces. 相似文献
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Jung-Chan Chang Sen-Yen Shaw 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(6):1670-1683
In this paper, we investigate the existence, uniqueness of solutions to boundary Cauchy equations with infinite delay, which are more general than the previous studies. The conclusions are applied to an age dependent population with delay in the birth process. 相似文献
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Chunshan Zhao 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(11):4188-4199
We continue our work (Y. Li, C. Zhao, Locating the peaks of least-energy solutions to a quasilinear elliptic Neumann problem, J. Math. Anal. Appl. 336 (2007) 1368-1383) to study the shape of least-energy solutions to the quasilinear problem εmΔmu−um−1+f(u)=0 with homogeneous Neumann boundary condition. In this paper we focus on the case 1<m<2 as a complement to our previous work on the case m≥2. We use an intrinsic variation method to show that as the case m≥2, when ε→0+, the global maximum point Pε of least-energy solutions goes to a point on the boundary ∂Ω at a rate of o(ε) and this point on the boundary approaches a global maximum point of mean curvature of ∂Ω. 相似文献
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In this paper, we prove that strongly convex space and almost locally uniformly rotund space, very convex space and weakly almost locally uniformly rotund space are respectively equivalent. We also investigate a few properties of k-strongly convex space and k-very convex space, and discuss the applications of strongly convex space and very convex space in approximation theory. 相似文献
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The closed Dirichlet problem for an elliptic-hyperbolic equation arising in linearizing the Monge-Ampère type equation is shown to admit a distributional solution by using an a-b-c integral method. 相似文献
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Chun LiZeng-Qi Ou Chun-Lei Tang 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(4):2262-2272
Some existence theorems are obtained for periodic and subharmonic solutions of a class of non-autonomous Hamiltonian systems. Our technical approach is based on a version of the Local Linking Theorem, and the Generalized Mountain Pass Theorem. 相似文献
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In this paper, the geometric meaning of (α,β)-norms is made clear. On this basis, a new class of Finsler metrics called general (α,β)-metrics are introduced, which are defined by a Riemannian metric and a 1-form. These metrics not only generalize (α,β)-metrics naturally, but also include some metrics structured by R. Bryant. The spray coefficients formula of some kinds of general (α,β)-metrics is given and the projective flatness is also discussed. 相似文献
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Cédric Bentz 《Discrete Applied Mathematics》2008,156(10):1908-1917
Given an edge- or vertex-weighted graph or digraph and a list of source-sink pairs, the minimum multicut problem consists in selecting a minimum weight set of edges or vertices whose removal leaves no path from each source to the corresponding sink. This is a classical NP-hard problem, and we show that the edge version becomes tractable in bounded tree-width graphs if the number of source-sink pairs is fixed, but remains NP-hard in directed acyclic graphs and APX-hard in bounded tree-width and bounded degree unweighted digraphs. The vertex version, although tractable in trees, is proved to be NP-hard in unweighted cacti of bounded degree and bounded path-width. 相似文献