Results 21 to 30 of about 317,499 (205)

Nehari manifold optimization and its application for finding unstable solutions of semilinear elliptic PDEs [PDF]

arXiv
A 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-saddles of this functional are local minimizers of the same functional restricted on the associated
Zhaoxing Chen, Wei Liu, Ziqing Xie, Wenfan Yi   +3 more
arxiv   +4 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
doaj   +4 more sources

Nehari manifold approach for a singular multi-phase variable exponent problem [PDF]

arXiv
This paper is concerned with a singular multi-phase problem with variable singularities. The main tool used is the Nehari manifold approach. Existence of at least two positive solutions with positive-negative energy levels are obtained.
Mustafa Avcı
arxiv   +5 more sources

Sign changing solution for a double phase problem with nonlinear boundary condition via the Nehari manifold [PDF]

arXiv, 2020
In this paper we study quasilinear elliptic equations driven by the so-called double phase operator and with a nonlinear boundary condition. Due to the lack of regularity, we prove the existence of multiple solutions by applying the Nehari manifold method along with truncation and comparison techniques and critical point theory.
Leszek Gasiński, Patrick Winkert
arxiv   +4 more sources

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
openalex   +4 more sources

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, Hicham Moussa, Lalla Saâdia Chadli   +2 more
doaj   +2 more sources

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
doaj   +2 more sources

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
doaj   +2 more sources

Existence of solutions for a singular double phase problem involving a $ψ$-Hilfer Fractional operator via Nehari Manifold [PDF]

arXiv, 2023
In this present paper, we investigate a new class of singular double phase $p$-Laplacian equation problems with a $\psi$-Hilfer fractional operator combined from a parametric term. Motivated by the fibering method using the Nehari manifold, we discuss the existence of at least two weak solutions to such problems when the parameter is small enough ...
J. Vanterler da C. Sousa, Karla Katerine Barboza de Lima, Leandro S. Tavares   +2 more
arxiv   +3 more sources

Further applications of the Nehari manifold method to functionals in $C^1(X \setminus \{0\})$ [PDF]

arXiv
We proceed with the study of the Nehari manifold method for functionals in $C^1(X \setminus \{0\})$, where $X$ is a Banach space. We deal now with functionals whose fibering maps have two critical points (a minimiser followed by a maximiser). Under some additional conditions we show that the Nehari manifold method provides us with the ground state ...
Edir Junior Ferreira Leite, Humberto Ramos Quoirin, Kaye Silva   +2 more
arxiv   +3 more sources