Results 51 to 60 of about 317,499 (205)

Nehari manifold approach for fractional Kirchhoff problems with extremal value of the parameter

Fractional Calculus and Applied Analysis, 2023
In this work we study the following nonlocal problem \begin{equation*} \left\{ \begin{aligned} M(\|u\|^2_X)(-Δ)^s u&= λ{f(x)}|u|^{γ-2}u+{g(x)}|u|^{p-2}u &&\mbox{in}\ \ Ω, u&=0 &&\mbox{on}\ \ \mathbb R^N\setminus Ω, \end{aligned} \right.
Mishra, P. K., Tripathi, V. M.
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The Nehari manifold for a singular elliptic equation involving the fractional Laplace operator [PDF]

Fractional Differential Calculus, 2016
Abdeljab ar Ghanmi, Kamel Saoudi
openalex   +3 more sources

On the existence of ground states of an equation of Schrödinger–Poisson–Slater type

Comptes Rendus. Mathématique, 2021
We study the existence of ground states of a Schrödinger–Poisson–Slater type equation with pure power nonlinearity. By carrying out the constrained minimization on a special manifold, which is a combination of the Pohozaev manifold and Nehari manifold ...
Lei, Chunyu, Lei, Yutian
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The Nehari manifold for systems of nonlinear elliptic equations [PDF]

Nonlinear Analysis: Theory, Methods & Applications, 2006
Abstract This paper deals with the existence and multiplicity results of nonlocal positive solutions to the following system: - Δ p u = λ | u | p 1 - 2 u + ( α + 1 ) u | u | α - 1 | v | β + 1 , - Δ q v = μ | v | q - 2 v + ( β + 1 ) | u |
Adriouch, K., El Hamidi, Abdallah
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Existence of Positive Ground State Solutions for Fractional Choquard Systems in Subcritical and Critical Cases

Mathematics, 2023
We investigate a class of fractional linearly coupled Choquard systems. For the subcritical case and all critical cases, we prove the existence, nonexistence and symmetry of positive ground state solutions of systems, by using the Nehari manifold method,
Huiqin Lu, Kexin Ouyang
doaj   +1 more source

Existence and multiplicity of solutions to fractional p-Laplacian systems with concave–convex nonlinearities [PDF]

Bulletin of Mathematical Sciences, 2020
This paper is concerned with a fractional p-Laplacian system with both concave–convex nonlinearities. The existence and multiplicity results of positive solutions are obtained by variational methods and the Nehari manifold.
Hamed Alsulami, Mokhtar Kirane, Shabab Alhodily, Tareq Saeed, Nemat Nyamoradi   +4 more
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Nehari Manifold for Fractional Kirchhoff Systems with Critical Nonlinearity

Milan Journal of Mathematics, 2019
In this paper, we show the existence and multiplicity of positive solutions of the following fractional Kirchhoff system\\ \begin{equation} \left\{ \begin{array}{rllll} \mc L_M(u)&= f(x)|u|^{q-2}u+ \frac{2 }{ + }\left|u\right|^{ -2}u|v|^ & \text{in } ,\\ \mc L_M(v)&= g(x)|v|^{q-2}v+ \frac{2 }{ + }\left|u\right|^ |v|^{ -2}v ...
do Ó, J.M., Giacomoni, Jacques, Mishra, P.K.   +2 more
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Nehari manifold for a singular fractional problem driven by a general non-local integrodifferential operator

Discrete and Continuous Dynamical Systems. Series A
Rym Chammem, Abdeljabbar Ghanmi, Mahfoudh Mechergui   +2 more
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On a class of nonlocal nonlinear Schrödinger equations with potential well

Advances in Nonlinear Analysis, 2019
In this paper we investigate the existence, multiplicity and asymptotic behavior of positive solution for the nonlocal nonlinear Schrödinger equations. We exploiting the relationship between the Nehari manifold and eigenvalue problems to discuss how the ...
Wu Tsung-fang
doaj   +1 more source

Gap solitons in almost periodic one-dimensional structures [PDF]

, 2015
We consider almost periodic stationary nonlinear Schr\"odinger equations in dimension $1$. Under certain assumptions we prove the existence of nontrivial finite energy solutions in the strongly indefinite case.
Pankov, Alexander
core   +1 more source