Results 11 to 20 of about 145,855 (140)

Fractional minimization problem on the Nehari manifold [PDF]

Electronic Journal of Differential Equations, 2018
Summary: In the framework of fractional Sobolev space, using Nehari manifold and concentration compactness principle, we study a minimization problem in the whole space involving the fractional Laplacian. Firstly, we give a Lions type lemma in fractional Sobolev space, which is crucial in the proof of our main result.
Mei Yu, Meina Zhang, Xia Zhang
core   +6 more sources

Nehari manifold for degenerate logistic parabolic equations [PDF]

Electronic Journal of Differential Equations
In this  article we analyze the behavior of solutions to a degenerate logistic equation with a nonlinear term \(b(x)f(u)\) where the weight function \(b\) is  non-positive. We use variational techniques and the comparison principle to study the evolutionary dynamics. A crucial role is then played by the Nehari manifold, as we note how it changes as the
Juliana Fernandes, Liliane Maia
core   +6 more sources

On the Nehari manifold for a logarithmic fractional Schrödinger equation with possibly vanishing potentials [PDF]

Mathematica Bohemica, 2022
summary: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 ...
Le, Cong Nhan, Le, Xuan Truong
core   +3 more sources

Gluing approximate solutions of minimum type on the Nehari manifold

Electronic Journal of Differential Equations, 2001
Summary: In the last decade or so, variational gluing methods have been widely used to construct homoclinic and heteroclinic type solutions of nonlinear elliptic equations and Hamiltonian systems. This note is concerned with the procedure of gluing mountain-pass type solutions.
Yanyan Li, Zhi-Qiang Wang
core   +4 more sources

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

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, Yutian, Yutian Lei, Chunyu Lei, Lei, Chunyu   +3 more
core   +3 more sources

Existence of Weak Solutions for Nonlinear Time-Fractional -Laplace Problems [PDF]

Journal of Applied Mathematics, 2018
The existence of weak solution for p-Laplace problem is studied in the paper. By exploiting the relationship between the Nehari manifold and fibering maps and combining the compact imbedding theorem and the behavior of Palais-Smale sequences in the ...
Meilan Qiu, Liquan Mei, Qiu, Meilan, Mei, Liquan   +3 more
core   +3 more sources

Critical Fractional p‐Laplacian System with Negative Exponents

Journal of Function Spaces, Volume 2023, Issue 1, 2023., 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 respect to a sufficiently small parameter.
Qinghao Zhu, Jianming Qi, Baowei Feng
wiley   +2 more sources

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.
Fernandes, Juliana, Maia, Liliane A.
openaire   +3 more sources

Multiple Solutions for Singular Systems with Sign‐Changing Weight, Nonlinear Singularities and Critical Exponent

International Journal of Differential Equations, Volume 2024, Issue 1, 2024.
This 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. By using variational methods, the Nehari manifold, and under sufficient conditions on the parameter η which represent some physical meanings, we prove some ...
Mohammed El Mokhtar Ould El Mokhtar, Saleh Fahad Aljurbua, Md. Kamrujjaman   +2 more
wiley   +2 more sources

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 $Δ_{p(x)}u= div(|\nabla u|^{p(x)-2}\nabla u)$, where $p(x)$ is a nonconstant continuous function, \begin{equation} \nonumber {(\rm P_λ)} \left\{\begin{aligned} - Δ_{p(x)} u & = a(x)|u|^{q(x)-2}u(x)+ \frac{λb(x)}{u^{δ(x)}} \quad\mbox{in}\,Ω,\\ u &>0 \quad\mbox{in ...
Dušan D. Repovš, Kamel Saoudi
openaire   +5 more sources