Results 1 to 10 of about 2,242 (124)

The Nehari Manifold for p-Laplacian Equation with Dirichlet Boundary Condition

Nonlinear Analysis, 2007
The Nehari manifold for the equation −∆pu(x) = λu(x)|u(x)| p−2 + b(x)|u(x)| γ−2u(x) for x ∈ Ω together with Dirichlet boundary condition is investigated in the case where 0 < γ < p.
G. A. Afrouzi, S. Mahdavi, Z. Naghizadeh
doaj   +3 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

Solutions for the quasi-linear elliptic problems involving the critical Sobolev exponent. [PDF]

J Inequal Appl, 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.
Sang Y, Guo S.
europepmc   +2 more sources

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

Mathematica Bohemica, 2022
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 solution.
Cong Nhan Le, Xuan Truong Le
doaj   +2 more sources

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

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

On branches of positive solutions for p-Laplacian problems at the extreme value of Nehari manifold method

, 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
core   +2 more sources

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

International Journal of Differential Equations
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.
Mohammed El Mokhtar Ould El Mokhtar, Saleh Fahad Aljurbua   +1 more
doaj   +2 more sources

Existence of multiple solutions for a p-Kirchhoff problem with nonlinear boundary conditions. [PDF]

ScientificWorldJournal, 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 ...
Xiu Z, Chen C.
europepmc   +2 more sources

Nehari manifold for degenerate logistic parabolic equations

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.
Juliana Fernandes, Liliane Maia
doaj   +2 more sources