The Nehari manifold for fractional systems involving critical nonlinearities
Communications on Pure and Applied Analysis, 2016 We study the combined effect of concave and convex nonlinearities on the number of positive solutions for a fractional system involving critical Sobolev exponents.
He, Xiaoming +2 more
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Solutions for the quasi-linear elliptic problems involving the critical Sobolev exponent. [PDF]
J Inequal Appl, 2017 In this article, we study the existence and multiplicity of positive solutions for the quasi-linear elliptic problems involving critical Sobolev exponent and a Hardy term.
Sang Y, Guo S.
europepmc +2 more sources
The Nehari manifold method for discrete fractional p-Laplacian equations [PDF]
Advances in Difference Equations, 2020 The aim of this paper is to investigate the multiplicity of homoclinic solutions for a discrete fractional difference equation. First, we give a variational framework to a discrete fractional p-Laplacian equation.
Xuewei Ju, Hu Die, Mingqi Xiang
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Existence of multiple solutions for a p-Kirchhoff problem with nonlinear boundary conditions. [PDF]
ScientificWorldJournal, 2013 The paper considers the existence of multiple solutions of the singular nonlocal elliptic problem , , = , on , where , . By the variational method on the Nehari manifold, we prove that the problem has at least two positive solutions when some ...
Xiu Z, Chen C.
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Nehari manifold for degenerate logistic parabolic equations
Electronic Journal of Differential EquationsIn this article we analyze the behavior of solutions to a degenerate logistic equation with a nonlinear term $b(x)f(u)$ where the weight function $b$ is non-positive.
Juliana Fernandes, Liliane Maia
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Ground state solution of a nonlocal boundary-value problem
Electronic Journal of Differential Equations, 2013 In this article, we apply the Nehari manifold method to study the Kirchhoff type equation $$ -\Big(a+b\int_\Omega|\nabla u|^2dx\Big)\Delta u=f(x,u) $$ subject to Dirichlet boundary conditions.
Cyril Joel Batkam
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The Nehari Manifold for p-Laplacian Equation with Dirichlet Boundary Condition
Nonlinear Analysis, 2007 The Nehari manifold for the equation −∆pu(x) = λu(x)|u(x)| p−2 + b(x)|u(x)| γ−2u(x) for x ∈ Ω together with Dirichlet boundary condition is investigated in the case where 0 < γ < p.
G. A. Afrouzi, S. Mahdavi, Z. Naghizadeh
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Fractional minimization problem on the Nehari manifold
Electronic Journal of Differential Equations, 2018 In the framework of fractional Sobolev space, using Nehari manifold and concentration compactness principle, we study a minimization problem in the whole space involving the fractional Laplacian.
Mei Yu, Meina Zhang, Xia Zhang
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Gluing approximate solutions of minimum type on the Nehari manifold
Electronic Journal of Differential Equations, 2001 In the last decade or so, variational gluing methods have been widely used to construct homoclinic and heteroclinic type solutions of nonlinear elliptic equations and Hamiltonian systems.
Yanyan Li, Zhi-Qiang Wang
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NON-NEHARI MANIFOLD METHOD FOR SUPERLINEAR SCHRÖDINGER EQUATION [PDF]
Taiwanese Journal of Mathematics, 2014 We consider the boundary value problem \begin{equation} \label{(0.1)} \left\{ \begin{array}{ll} -\triangle u+V(x)u=f(x, u), \ \ \ \ & x\in \Omega,\\ u=0, \ \ \ \ & x\in \partial\Omega, \end{array} \right. \end{equation} where $ \Omega \subset \mathbb R^N$ be a bounded domain, $\inf_{\Omega}V(x)>-\infty$, $f$ is a superlinear, subcritical ...
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