Results 1 to 10 of about 13,774 (162)

Inhomogeneous Neumann problem with critical Sobolev exponent [PDF]

Advances in Nonlinear Analysis, 2012
We investigate the solvability of the inhomogeneous Neumann problem involving the critical Sobolev exponent. In particular, we discuss the impact of the shape of the graph of the coefficient of the critical exponent on the existence of a solution.
Chabrowski Jan
doaj   +3 more sources

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

Journal of Inequalities and Applications, 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.
Yanbin Sang, Siman Guo
doaj   +2 more sources

On a singular nonlinear Neumann problem [PDF]

Opuscula Mathematica, 2014
We investigate the solvability of the Neumann problem involving two critical exponents: Sobolev and Hardy-Sobolev. We establish the existence of a solution in three cases: \(\text{(i)}\;\ 2\lt p+1\lt 2^*(s),\) \(\text{(ii)}\;\ p+1=2^*(s)\) and \(\text ...
Jan Chabrowski
doaj   +1 more source

Existence of solution for a quasilinear elliptic Neumann problem involving multiple critical exponents

Boundary Value Problems, 2020
In this paper, we study the Neumann boundary value problem to a quasilinear elliptic equation with the critical Sobolev exponent and critical Hardy–Sobolev exponent, and prove the existence of nontrivial nonnegative solution by means of variational ...
Yuanxiao Li, Xiying Wang
doaj   +1 more source

Problem with Critical Sobolev Exponent and with Weight [PDF]

Chinese Annals of Mathematics, Series B, 2007
We study existence results for a problem with criticical Sobolev exponent and with a positive weight.
Hadiji, Rejeb, Yazidi, Habib
openaire   +5 more sources

Groundstates for Choquard type equations with weighted potentials and Hardy–Littlewood–Sobolev lower critical exponent

Advances in Nonlinear Analysis, 2021
We are concerned with a class of Choquard type equations with weighted potentials and Hardy–Littlewood–Sobolev lower critical ...
Zhou Shuai, Liu Zhisu, Zhang Jianjun
doaj   +1 more source

On Hamiltonian systems with critical Sobolev exponents

Journal of Differential Equations, 2023
26 ...
Angelo Guimarães, Ederson Moreira dos Santos   +1 more
openaire   +3 more sources

Weighted critical exponents of Sobolev-type embeddings for radial functions

Advanced Nonlinear Studies, 2022
In this article, we prove the upper weighted critical exponents for some embeddings from weighted Sobolev spaces of radial functions into weighted Lebesgue spaces. We also consider the lower critical exponent for certain embedding.
Su Jiabao, Wang Cong
doaj   +1 more source

Strongly indefinite systems with critical Sobolev exponents [PDF]

Transactions of the American Mathematical Society, 1998
Let \(\Omega\) be a bounded domain in \(\mathbb R^n\) (\(n\geq 4\)) with smooth boundary, \(\lambda, \mu\in\mathbb R\), and \(p\geq q>1\). The authors investigate the solvability of the system \[ -\Delta v=\lambda u+| u|^{p-1}u,\quad -\Delta u=\mu v+| v|^{q-1}v\quad \text{in } \Omega,\qquad u=0=v\quad\text{on }\partial\Omega, \] in case that \({1\over ...
MITIDIERI, ENZO, HULSHOF J, VAN DER VORST R.   +2 more
openaire   +4 more sources

Existence of Two Solutions for a Critical Elliptic Problem with Nonlocal Term in ℝ4

Journal of Function Spaces, 2022
In this paper, we prove the existence of two positive solutions for a critical elliptic problem with nonlocal term and Sobolev exponent in dimension four.
Khadidja Sabri, Atika Matallah, Safia Benmansour, Mohammed El Mokhtar Ould El Mokhtar   +3 more
doaj   +1 more source