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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On the Nehari manifold for a logarithmic fractional Schrödinger equation with possibly vanishing potentials [PDF]
Mathematica Bohemica, 2022 We study a class of logarithmic fractional Schrödinger equations with possibly vanishing potentials. By using the fibrering maps and the Nehari manifold we obtain the existence of at least one nontrivial solution.
Cong Nhan Le, Xuan Truong Le
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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 ...
Xianhua Tang
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The Nehari manifold for fractional systems involving critical nonlinearities
Communications on Pure and Applied Analysis, 2015 To appear in Commun.
Xiaoming He +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.
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Second-order derivative of domain-dependent functionals along Nehari manifold trajectories [PDF]
ESAIM: Control, Optimisation and Calculus of Variations, 2019 Assume that a family of domain-dependent functionals EΩt possesses a corresponding family of least energy critical points ut which can be found as (possibly nonunique) minimizers of EΩt over the associated Nehari manifold N(Ωt). We obtain a formula for the second-order derivative of EΩt with respect to t along Nehari manifold trajectories of the form ...
Vladimir Bobkov, Sergey Kolonitskii
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Nehari manifold approach for superlinear double phase problems with variable exponents
Annali di Matematica Pura ed Applicata (1923 -), 2022 AbstractIn this paper we consider quasilinear elliptic equations driven by the variable exponent double phase operator with superlinear right-hand sides. Under very general assumptions on the nonlinearity, we prove a multiplicity result for such problems whereby we show the existence of a positive solution, a negative one and a solution with changing ...
Ángel Crespo‐Blanco, Patrick Winkert
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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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Non-Nehari manifold method for asymptotically periodic Schrödinger equations [PDF]
Science China Mathematics, 2014 We consider the semilinear Schr dinger equation $$ \left\{ \begin{array}{ll} -\triangle u+V(x)u=f(x, u), \ \ \ \ x\in {\R}^{N}, u\in H^{1}({\R}^{N}), \end{array} \right. $$ where $f$ is a superlinear, subcritical nonlinearity. We mainly study the case where $V(x)=V_0(x)+V_1(x)$, $V_0\in C(\mathbb{R}^N)$, $V_0(x)$ is 1-periodic in each of $x_1, x_2 ...
Xianhua Tang
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The Nehari manifold for a semilinear elliptic problem with the nonlinear boundary condition
Journal of Mathematical Analysis and Applications, 2012 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 .
Jinguo Zhang, Xiaochun Liu
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