Results 11 to 20 of about 521 (162)

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
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On p-Laplace Equations with Singular Nonlinearities and Critical Sobolev Exponent

Journal of Function Spaces, 2022
In this paper, we deal with p-Laplace equations with singular nonlinearities and critical Sobolev exponent. By using the Nehari manifold, Mountain Pass theorem, and Maximum principle theorem, we prove the existence of at least four distinct nontrivial ...
Mohammed El Mokhtar ould El Mokhtar
doaj   +2 more sources

NON-NEHARI-MANIFOLD METHOD FOR ASYMPTOTICALLY LINEAR SCHRÖDINGER EQUATION [PDF]

Journal of the Australian Mathematical Society, 2014
AbstractWe consider the semilinear Schrödinger equation$$\begin{eqnarray}\left\{\begin{array}{@{}l@{}}-\triangle u+V(x)u=f(x,u),\quad x\in \mathbb{R}^{N},\\ u\in H^{1}(\mathbb{R}^{N}),\end{array}\right.\end{eqnarray}$$where$f(x,u)$is asymptotically linear with respect to$u$,$V(x)$is 1-periodic in each of$x_{1},x_{2},\dots ,x_{N}$and$\sup [{\it\sigma}(-\
Xianhua Tang
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The Nehari manifold for aψ-Hilfer fractionalp-Laplacian

Applicable Analysis, 2021
In this paper, we discuss the existence and non-existence of weak solutions to the non-linear problem with a fractional p-Laplacian introduced by the ψ-Hilfer fractional operator, by combining the ...
J. Vanterler da C. Sousa, Jiabin Zuo, Donal O’Regan   +2 more
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The Nehari manifold for elliptic equation involving the square root of the Laplacian

Journal of Differential Equations, 2011
AbstractIn this paper, we introduce the Nehari manifold for elliptic problems involving the square root of the Laplacian. We use it to establish the existence of solutions and multiple solutions for some nonlinear elliptic problem with sign-changing weight. We also establish some bifurcation results and non-existence results.
Xiaohui Yu
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Existence of positive ground solutions for biharmonic equations via Pohožaev-Nehari manifold [PDF]

Topological Methods in Nonlinear Analysis, 2018
We investigate the following nonlinear biharmonic equations with pure power nonlinearities: \begin{equation*} \begin{cases} \triangle^2u-\triangle u+V(x)u= u^{p-1}u &\text{in } \mathbb{R}^N,\\ u> 0 &\text{for } u\in H^2(\mathbb{R}^N), \end{cases} \end{equation*} where $2< p< 2^*={2N}/({N-4})$.
Liping Xu, Haibo Chen
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The Nehari manifold for a degenerate logistic parabolic equation

, 2023
The present paper analyses the behavior of solutions to a degenerate logistic equation with a nonlinear term of the form b(x)f(u), where the weight function b is assumed to be nonpositive. We exploit variational techniques and comparison principle in order to study the evolutionary dynamics.
Juliana Dumêt Fernandes, Liliane A. Maia   +1 more
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Some applications of the Nehari manifold method to functionals in $C^1(X \setminus \{0\})$ [PDF]

Calculus of Variations and Partial Differential Equations
Given a real Banach space $X$, we show that the Nehari manifold method can be applied to functionals which are $C^1$ in $X \setminus \{0\}$. In particular we deal with functionals that can be unbounded near $0$, and prove the existence of a ground state and infinitely many critical points for such functionals.
Edir Ferreira Leite, Humberto Ramos Quoirin, Kaye Silva   +2 more
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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   +3 more sources

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
doaj   +2 more sources