Results 21 to 30 of about 24,259 (189)

Existence and multiplicity of nontrivial solutions for Schrödinger-Poisson systems on bounded domains

Boundary Value Problems, 2018
In this paper, we concern with the following Schrödinger-Poisson system: {−Δu+ϕu=f(x,u),x∈Ω,−Δϕ=u2,x∈Ω,u=ϕ=0,x∈∂Ω, $$ \textstyle\begin{cases} -\Delta u+\phi u = f(x,u) , & x\in\Omega,\\ -\Delta\phi=u^{2}, & x\in\Omega,\\ u=\phi=0, & x \in\partial\Omega, \
Belal Almuaalemi, Haibo Chen, Sofiane Khoutir   +2 more
doaj   +1 more source

Existence and Multiplicity of Fast Homoclinic Solutions for a Class of Nonlinear Second-Order Nonautonomous Systems in a Weighted Sobolev Space

Journal of Function Spaces, 2015
This paper is concerned with the following nonlinear second-order nonautonomous problem: ü(t)+q(t)u̇(t)-∇K(t,u(t))+∇W(t,u(t))=0, where t∈R, u∈RN, and K, W∈C1(R×RN,R) are not periodic in t and q:R→R is a continuous function and Q(t)=∫0t‍q(s)ds with lim|t|
Qiongfen Zhang, Yuan Li
doaj   +1 more source

A Mountain Pass-type Theorem for Vector-valued Functions [PDF]

Set-Valued and Variational Analysis, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bednarczuk, E, Miglierina, Enrico, Molho, E.   +2 more
openaire   +3 more sources

Existence of at least one nontrivial solution for a class of problems involving both p(x)-Laplacian and p(x)-Biharmonic

پژوهش‌های ریاضی, 2022
We investigate the existence of a weak nontrivial solution for the following problem. Our analysis is generally bathed on discussions of variational based on the Mountain Pass theorem and some recent theories one the generalized Lebesgue-Sobolev space ...
Atieh Ramzannia Jalali, Ghasem Alizadeh Afrouzi   +1 more
doaj  

The Existence Result for a p-Kirchhoff-Type Problem Involving Critical Sobolev Exponent

Journal of Function Spaces, 2023
In this paper, by using the mountain pass theorem and the concentration compactness principle, we prove the existence of a positive solution for a p-Kirchhoff-type problem with critical Sobolev exponent.
Hayat Benchira, Atika Matallah, Mohammed El Mokhtar Ould El Mokhtar, Khadija Sabri   +3 more
doaj   +1 more source

A Dirichlet problem with asymptotically linear and changing sign nonlinearity [PDF]

, 2003
This paper deals with the problem of finding positive solutions to the equation ¡¢u = g(x; u) on a bounded domain ­; with Dirichlet boundary conditions. The function g can change sign and has asymptotically linear behaviour.
Lucia, Marcello, Magrone, Paola, Zhou, Huan-Song   +2 more
core   +2 more sources

A variant of mountain pass theorem

Differential and Integral Equations, 2013
An existence result for a critical point of mountain-pass type, where the classical Palais--Smale condition is not required, is presented. A multiple-critical-point result is then obtained. As an application, the existence of two positive classical solutions for two-point boundary-value problems, without assuming any asymptotic condition on the ...
Bonanno, Gabriele, D'Aguì, Giuseppina
openaire   +2 more sources

Existence and Multiplicity of Homoclinic Orbits for Second-Order Hamiltonian Systems with Superquadratic Potential

Abstract and Applied Analysis, 2013
We investigate the existence and multiplicity of homoclinic orbits for second-order Hamiltonian systems with local superquadratic potential by using the Mountain Pass Theorem and the Fountain Theorem, respectively.
Ying Lv, Chun-Lei Tang
doaj   +1 more source

Multiplicity of positive solutions for second order quasilinear equations [PDF]

Mathematica Bohemica, 2020
We discuss the existence and multiplicity of positive solutions for a class of second order quasilinear equations. To obtain our results we will use the Ekeland variational principle and the Mountain Pass Theorem.
Dahmane Bouafia, Toufik Moussaoui, Donal O'Regan   +2 more
doaj   +1 more source

Existence and Multiplicity of Solutions for a Class of Anisotropic Double Phase Problems

Advances in Mathematical Physics, 2020
We consider the following double phase problem with variable exponents: −div∇upx−2∇u+ax∇uqx−2∇u=λfx,u in Ω,u=0, on ∂Ω. By using the mountain pass theorem, we get the existence results of weak solutions for the aforementioned problem under some ...
Jie Yang, Haibo Chen, Senli Liu
doaj   +1 more source