Solutions for the quasi-linear elliptic problems involving the critical Sobolev exponent [PDF]
Journal of Inequalities and Applications, 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.
Yanbin Sang, Siman Guo
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The Nehari Manifold for a Class of Singular $\psi$-Riemann-Liouville Fractional with $p$-Laplacian Operator Differential Equations [PDF]
Advances in Applied Mathematics and Mechanics. Using Nehari manifold method combined with fibring maps, we show the existence of nontrivial, weak, positive solutions of the nonlinear ψ -Riemann-Liouville fractional boundary value problem involving the p -Laplacian operator, given ...
Samah Horrigue +2 more
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Ground State Solutions for a Nonlocal System in Fractional Orlicz-Sobolev Spaces
International Journal of Differential Equations, 2022 We consider an elliptic system driven by the fractional a.-Laplacian operator, with Dirichlet boundary conditions type. By using the Nehari manifold approach, we get a nontrivial ground state solution on fractional Orlicz–Sobolev spaces.
Hamza El-Houari +2 more
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The Nehari manifold approach for singular equations involving the p(x)-Laplace operator [PDF]
Complex Variables and Elliptic Equations, 2021 We study the following singular problem involving the p(x)-Laplace operator , where is a nonconstant continuous function, Here, Ω is a bounded domain in with -boundary, λ is a positive parameter, are positive weight functions with compact support in Ω ...
Dušan D. Repovš, Kamel Saoudi
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Existence of Multiple Solutions for a -Kirchhoff Problem with Nonlinear Boundary Conditions [PDF]
The Scientific World Journal, 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 ...
Zonghu Xiu, Caisheng Chen
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On branches of positive solutions for p-Laplacian problems at the extreme value of Nehari manifold method [PDF]
, 2017 This paper is concerned with variational continuation of branches of solutions for nonlinear boundary value problems, which involve the p-Laplacian, the indefinite nonlinearity, and depend on the real parameter $\lambda$.
Il'yasov, Yavdat, Silva, Kaye
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Nehari manifold optimization and its application for finding unstable solutions of semilinear elliptic PDEs [PDF]
SIAM Journal on Scientific ComputingA Nehari manifold optimization method (NMOM) is introduced for finding 1-saddles, i.e., saddle points with the Morse index equal to one, of a generic nonlinear functional in Hilbert spaces. Actually, it is based on the variational characterization that 1-
Zhaoxing Chen +3 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 ...
Xianhua Tang
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Critical Fractional p-Laplacian System with Negative Exponents
Journal of Function Spaces, 2023 In this paper, we consider a class of fractional p-Laplacian problems with critical and negative exponents. By decomposition of the Nehari manifold, the existence and multiplicity of nontrivial solutions for the above problems are established with ...
Qinghao Zhu, Jianming Qi
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International Journal of Differential EquationsThis paper is an attempt to establish the existence and multiplicity results of nontrivial solutions to singular systems with sign-changing weight, nonlinear singularities, and critical exponent.
Mohammed El Mokhtar Ould El Mokhtar +1 more
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