共查询到20条相似文献,搜索用时 15 毫秒
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In this paper we study nonlinear Neumann problems driven by the p ‐Laplacian and having a nonsmooth potential. Using techniques from the nonsmooth critical point theory, we prove two existence theorems and a multiplicity result. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Summary
Existence theorems for nonlinear Neumann problems with inhomogeneous boundary conditions are established. It is then investigated under which conditions the solutions are uniformly bounded. Uniqueness results for positive solutions are given and the asymptotic behavior of the solutions of the corresponding parabolic equation is discussed. The main tools are fixed point theorems and the method of upper and lower solutions. 相似文献
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Summary. We study a new class of backward stochastic differential equations, which involves the integral with respect to a continuous
increasing process. This allows us to give a probabilistic formula for solutions of semilinear partial differential equations
with Neumann boundary condition, where the boundary condition itself is nonlinear. We consider both parabolic and elliptic
equations.
Received: 27 September 1996 / In revised form: 1 December 1997 相似文献
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Qingliu Yao 《Applied mathematics and computation》2010,217(6):2301-2306
Two successively iterative sequences are constructed for computing solutions of the nonlinear Neumann boundary value problems with time singularity. The sequences start off with some constants. Main tool is the fixed point theorem of increasing operator on the order interval. By considering convergence of the sequences, we prove the existence of nontrivial sign-changing solutions. 相似文献
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Jaeyoung Byeon 《Journal of Differential Equations》2008,244(10):2473-2497
Let Ω be a bounded domain in Rn, n?3, with the boundary ∂Ω∈C3. We consider the following singularly perturbed nonlinear elliptic problem on Ω
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Pigong Han Zhaoxia Liu 《Calculus of Variations and Partial Differential Equations》2007,30(3):315-352
Let Ω be an open bounded domain in with smooth boundary . We are concerned with the critical Neumann problem
where and Q(x) is a positive continuous function on . Using Moser iteration, we give an asymptotic characterization of solutions for (*) at the origin. Under some conditions
on Q, μ, we, by means of a variational method, prove that there exists such that for every , problem (*) has a positive solution and a pair of sign-changing solutions. 相似文献
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We consider a nonlinear elliptic Neumann problem driven by the p-Laplacian with a reaction that involves the combined effects of a ??concave?? and of a ??convex?? terms. The convex term (p-superlinear term) need not satisfy the Ambrosetti?CRabinowitz condition. Employing variational methods based on the critical point theory together with truncation techniques, we prove a bifurcation type theorem for the equation. 相似文献
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Entropy solutions for nonlinear elliptic anisotropic problems with homogeneous Neumann boundary condition
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This study is about a nonlinear anisotropic problem with homogeneous Neumann boundary condition. We first prove, by using the technic of monotone operators in Banach spaces, the existence of weak solution, and by approximation methods, we achieve a result of existence and uniqueness of entropy solution 相似文献
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Qingliu Yao 《Applied Mathematics Letters》2012,25(2):93-98
Allowing the nonlinear term to be singular with respect to both the time and space variables, we consider the positive solutions of a nonlinear Neumann boundary value problem. By constructing two height functions and estimating the integrations of these height functions, the existence and multiplicity of positive solutions are established. 相似文献
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Jan Chabrowski Zhi-Qiang Wang 《NoDEA : Nonlinear Differential Equations and Applications》2007,13(5-6):683-697
We consider the solvability of the Neumann problem for equation (1.1) in exterior domains in both cases: subcritical and critical.
We establish the existence of least energy solutions. In the subcritical case the coefficient
b(x) is allowed to have a potential well whose steepness is controlled by a parameter λ > 0. We show that least energy solutions
exhibit a tendency to concentrate to a solution of a nonlinear problem with mixed boundary value conditions. 相似文献
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Denis Bonheure Enrico Serra 《NoDEA : Nonlinear Differential Equations and Applications》2011,18(2):217-235
We consider a classical semilinear elliptic equation with Neumann boundary conditions on an annulus in R
N
. The nonlinear term is the product of a radially symmetric coefficient with a pure power. We prove that if the power is sufficiently
large, the problem admits at least three distinct positive and radial solutions. In case the coefficient is constant, we show
that none of the three solutions is constant. The methods are variational and are based on the study of a suitable limit problem. 相似文献
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We consider semilinear Neumann problems at resonance and prove existence and multiplicity theorems. The existence theorems allow resonance with respect to any eigenvalue of the negative Neumann Laplacian. The multiplicity theorems concern problems resonant at 0 (the principal eigenvalue) or at the first nonzero eigenvalue. Our approach uses tools from critical point theory and from Morse theory. 相似文献