Results 11 to 20 of about 1,665 (115)
, 2012 In this article, we study the nonlocal p(x)-Laplacian problem of the following form a(∫Ω1p(x)(|∇u|p(x)+|u|p(x))dx)(-div(|∇u|p(x)-2∇u)+|u|p(x)-2u)=b(∫ΩF(x,u)dx)f(x,u)inΩa∫Ω1p(x)(|∇u|p(x)+|u|p(x))dx|∇u|p(x)-2∂u∂ν=g(x,u)on∂Ω, where Ω is a smooth bounded ...
Erlin Guo, P. Zhao
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Species survival versus eigenvalues
Abstract and Applied Analysis, Volume 2004, Issue 2, Page 115-131, 2004., 2004 Mathematical models describing the behavior of hypothetical species in spatially heterogeneous environments are discussed and analyzed using the fibering method devised and developed by S. I. Pohozaev.
Luiz Antonio Ribeiro de Santana +2 more
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On a version of Trudinger-Moser inequality with M\"obius shift invariance [PDF]
, 2009 The paper raises a question about the optimal critical nonlinearity for the Sobolev space in two dimensions, connected to loss of compactness, and discusses the pertinent concentration compactness framework. We study properties of the improved version of
Adimurthi, Tintarev, K.
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An elliptic problem with critical exponent and positive Hardy potential
Abstract and Applied Analysis, Volume 2004, Issue 2, Page 91-98, 2004., 2004 We give the existence result and the vanishing order of the solution in 0 for the following equation: −Δu(x) + (μ/|x|2)u(x) = λu(x) + u2*−1(x), where x ∈ B1, μ > 0, and the potential μ/|x|2 − λ is positive in B1.
Shaowei Chen, Shujie Li
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Nehari-type ground state solutions for a Choquard equation with doubly critical exponents
Advances in Nonlinear Analysis, 2020 This paper deals with the following Choquard equation with a local nonlinear perturbation:
Chen Sitong, Tang Xianhua, Wei Jiuyang
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A Dirichlet problem with asymptotically linear and changing sign nonlinearity [PDF]
, 2003 This paper deals with the problem of finding positive solutions to the equation ¡¢u = g(x; u) on a bounded domain ; with Dirichlet boundary conditions. The function g can change sign and has asymptotically linear behaviour.
Lucia, Marcello +2 more
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Solutions for nonlinear variational inequalities with a nonsmooth potential
Abstract and Applied Analysis, Volume 2004, Issue 8, Page 635-649, 2004., 2004 First we examine a resonant variational inequality driven by the p‐Laplacian and with a nonsmooth potential. We prove the existence of a nontrivial solution. Then we use this existence theorem to obtain nontrivial positive solutions for a class of resonant elliptic equations involving the p‐Laplacian and a nonsmooth potential.
Michael E. Filippakis +1 more
wiley +1 more source
Perturbation results for some nonlinear equations involving fractional operators [PDF]
, 2012 By using a perturbation technique in critical point theory, we prove the existence of solutions for two types of nonlinear equations involving fractional differential operators.Comment: 14 ...
Secchi, Simone
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Multiple positive solutions for quasilinear elliptic problems with sign‐changing nonlinearities
Abstract and Applied Analysis, Volume 2004, Issue 12, Page 1047-1055, 2004., 2004 Using variational arguments, we prove some nonexistence and multiplicity results for positive solutions of a system of p‐Laplace equations of gradient form. Then we study a p‐Laplace‐type problem with nonlinear boundary conditions.
Julián Fernández Bonder
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Advances in Nonlinear Analysis, 2018 In this paper, we concern ourselves with the following Kirchhoff-type equations:
Xu Li-Ping, Chen Haibo
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