The Nehari Manifold for p-Laplacian Equation With Dirichlet Boundary Condition [PDF]
Nonlinear Analysis: Modelling and Control, 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. Exploiting the relationship between the Nehari manifold and fibrering maps (i.e., maps of the form of t → J(tu) where J is the Euler functional associated with the ...
Ghasem Afrouzi
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The Nehari Manifold for a Semilinear Elliptic Equation With a Sign-Changing Weight Function
Journal of Differential Equations, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Brown, K.J., Zhang, Yanping
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The Nehari Manifold for Fractional Systems Involving Critical Nonlinearities
Communications on Pure and Applied Analysis, 2016 To appear in Commun.
Xiaoming He +2 more
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The Nehari manifold for systems of nonlinear elliptic equations [PDF]
Nonlinear Analysis: Theory, Methods & Applications, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Adriouch, K., El Hamidi, Abdallah
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The Nehari manifold method for discrete fractional p-Laplacian equations [PDF]
Advances in Difference Equations, 2020 AbstractThe 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. Then two nontrivial and nonnegative homoclinic solutions are obtained by using the Nehari manifold method.
Xuewei Ju, Hu Die, Mingqi Xiang
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The Nehari Manifold for a Semilinear Elliptic Problem With the Nonlinear Boundary Condition
Journal of Mathematical Analysis and Applications, 2013 Abstract Using the Nehari manifold and fibering maps, we prove the existence theorem of the nonlinear boundary problem − Δ u + u = | u | p − 2 u for x ∈ Ω ; ∂ u ∂ n = λ | u | q − 2 u for x ∈ ∂ Ω on a bounded domain Ω ⊆ R N .
Xiaochun Liu, Jinguo Zhang
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The Nehari Manifold for Elliptic Equation Involving the Square Root of the Laplacian
Journal of Differential Equations, 2012 The author proves existence results for solutions of the equation \( A_{1/2}w=\mu w+b(x)| w| ^{\gamma -1}w\) posed in a smooth and bounded domain \(\Omega \) of \(\mathbb{R}^{N}\), \(N\geq 2\), with homogeneous Dirichlet boundary conditions on \(\partial \Omega \).
Xiaohui Yu
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Nehari manifold and fractional Dirichlet boundary value problem
Analysis and Mathematical Physics, 2022 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Vanterler da C. Sousa, J. +2 more
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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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Ground State Solutions of Schrödinger‐Kirchhoff Equations with Potentials Vanishing at Infinity
Journal of Function Spaces, Volume 2023, Issue 1, 2023., 2023 In this paper, we deal with the following Schrödinger‐Kirchhoff equation with potentials vanishing at infinity: −ε2a+εb∫ℝ3∇u2Δu+Vxu=Kxup−1u in ℝ3and u > 0, u ∈ H1(ℝ3), where V(x) ~ |x|−α and K(x) ~ |x|−β with 0 < α < 2, and β > 0. We first prove the existence of positive ground state solutions uε ∈ H1(ℝ3) under the assumption that σ < p < 5 for some σ =
Dongdong Sun, Baowei Feng
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