Results 21 to 30 of about 13,900 (197)

Fractional Laplacian equations with critical Sobolev exponent [PDF]

Revista Matemática Complutense, 2015
The paper under review extends in a fractional setting some results concerning the existence of nontrivial solutions for a class of nonlocal elliptic Dirichlet problems involving critical nonlinear terms. The basic analytic tool to establish the existence of a nontrivial solution is the linking method.
R. Servadei, E. Valdinoci
openaire   +5 more sources

On a Minimization Problem Involving the Critical Sobolev Exponent

Advanced Nonlinear Studies, 2007
Abstract Following [3] we study the following minimization problem: in any dimension n ≥ 4 and under suitable assumptions on a(x).
PRINARI F, VISCIGLIA, NICOLA
openaire   +3 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   +1 more source

On Coron's problem for the p-Laplacian [PDF]

, 2014
We prove that the critical problem for the $p$-Laplacian operator admits a nontrivial solution in annular shaped domains with sufficiently small inner hole.
Mercuri, Carlo, Sciunzi, Berardino, Squassina, Marco   +2 more
core   +1 more source

Existence and concentration behavior of solutions for a class of quasilinear elliptic equations with critical growth

Advances in Nonlinear Analysis, 2017
In this paper, we study a class of quasilinear elliptic equations involving the Sobolev critical ...
Teng Kaimin, Yang Xiaofeng
doaj   +1 more source

Boundary regularity for elliptic systems under a natural growth condition [PDF]

, 2010
We consider weak solutions $u \in u_0 + W^{1,2}_0(\Omega,R^N) \cap L^{\infty}(\Omega,R^N)$ of second order nonlinear elliptic systems of the type $- div a (\cdot, u, Du) = b(\cdot,u,Du)$ in $\Omega$ with an inhomogeneity satisfying a natural growth ...
Beck, Lisa
core   +3 more sources

Existence and multiplicity of solutions for Kirchhof-type problems with Sobolev–Hardy critical exponent

Boundary Value Problems, 2021
In this paper, we discuss a class of Kirchhof-type elliptic boundary value problem with Sobolev–Hardy critical exponent and apply the variational method to obtain one positive solution and two nontrivial solutions to the problem under certain conditions.
Hongsen Fan, Zhiying Deng
doaj   +1 more source

Schrödinger equation with critical Sobolev exponent

Differential and Integral Equations, 2004
In this paper we study the existence of solutions and their concentration phenomena of a singularly perturbed semilinear Schrodinger equation with the presence of the critical Sobolev exponent.
openaire   +4 more sources

A singular perturbed problem with critical Sobolev exponent

Topological Methods in Nonlinear Analysis, 2021
This paper deals with the following nonlinear elliptic problem \begin{equation}\label{eq0.1} -\varepsilon^2\Delta u+\omega V(x)u=u^{p}+u^{2^{*}-1},\quad u> 0\quad\text{in}\ \R^N, \end{equation} where $\omega\in\R^{+}$, $N\geq 3$, $p\in (1,2^{*}-1)$ with $2^{*}={2N}/({N-2})$, $\varepsilon> 0$ is a small parameter and $V(x)$ is a given function ...
Mengyao Chen, Qi Li
openaire   +2 more sources

Existence Results for Singular p-Biharmonic Problem with HARDY Potential and Critical Hardy-Sobolev Exponent

Axioms
In this article, we consider the singular p-biharmonic problem involving Hardy potential and critical Hardy–Sobolev exponent. Firstly, we study the existence of ground state solutions by using the minimization method on the associated Nehari manifold ...
Gurpreet Singh
doaj   +1 more source