Results 31 to 40 of about 13,793 (181)

A Nonlinear Elliptic PDE with Two Sobolev–Hardy Critical Exponents [PDF]

Archive for Rational Mechanics and Analysis, 2011
In this paper, we consider the following PDE involving two Sobolev-Hardy critical exponents, \label{0.1} {& u + \frac{u^{2^*(s_1)-1}}{|x|^{s_1}} + \frac{u^{2^*(s_2)-1}}{|x|^{s_2}} =0 \text{in} , & u=0 \qquad \text{on} , where $0 \le s_2 < s_1 \le 2$, $0 \ne \in \Bbb R$ and $0 \in \partial $.
Li, YanYan, Lin, Chang-Shou
openaire   +4 more sources

Hardy-Sobolev Equations on Compact Riemannian Manifolds

, 2014
Let (M,g) be a compact Riemannien Manifold of dimension n > 2, x_0 in M a fix and singular point and s in (0,2). We let 2*(s) = 2(n-s)/(n-2) be the critical Hardy-Sobolev exponent.
Jaber, Hassan
core   +1 more source

A Nonhomogeneous Fractional p-Kirchhoff Type Problem Involving Critical Exponent in ℝN

Advanced Nonlinear Studies, 2017
This paper concerns itself with the nonexistence and multiplicity of solutions for the following fractional Kirchhoff-type problem involving the critical Sobolev exponent:
Xiang Mingqi, Zhang Binlin, Zhang Xia
doaj   +1 more source

The concentration-compactness principles for Ws,p(·,·)(ℝN) and application

Advances in Nonlinear Analysis, 2020
We obtain a critical imbedding and then, concentration-compactness principles for fractional Sobolev spaces with variable exponents. As an application of these results, we obtain the existence of many solutions for a class of critical nonlocal problems ...
Ho Ky, Kim Yun-Ho
doaj   +1 more source

Multiplicity for critical and overcritical equations [PDF]

, 2008
On a Riemannian compact manifold, we give existence and multiplicity results for solutions of elliptic PDE by introducing isometry invariances. When the groups we used have finite orbits, we get multiplicity results for equations with the classical ...
Dellinger, Marie
core   +2 more sources

The existence of positive solutions for the Neumann problem of p-Laplacian elliptic systems with Sobolev critical exponent

Boundary Value Problems, 2022
The paper aims to consider a class of p-Laplacian elliptic systems with a double Sobolev critical exponent. We obtain the existence result of the above problem under the Neumann boundary for some suitable range of the parameters in the systems.
Bingyu Kou, Tianqing An
doaj   +1 more source

The Choquard Equation with Weighted Terms and Sobolev-Hardy Exponent

Journal of Function Spaces, 2018
We study a nonlinear Choquard equation with weighted terms and critical Sobolev-Hardy exponent. We apply variational methods and Lusternik-Schnirelmann category to prove the multiple positive solutions for this problem.
Yanbin Sang, Xiaorong Luo, Yongqing Wang
doaj   +1 more source

Multiplicity results for biharmonic equations involving multiple Rellich-type potentials and critical exponents

Boundary Value Problems, 2019
In this paper, a biharmonic equation is investigated, which involves multiple Rellich-type potentials and a critical Sobolev exponent. By using variational methods and analytical techniques, the existence and multiplicity of nontrivial solutions to the ...
Jinguo Zhang, Tsing-San Hsu
doaj   +1 more source

Spectral Methods in PDE

, 2010
This is to review some recent progress in PDE. The emphasis is on (energy) supercritical nonlinear Schr\"odinger equations. The methods are applicable to other nonlinear equations.Comment: This is an invited contribution to Milan J.
Wang, Wei-Min
core   +1 more source

Normalized solutions for a fractional coupled critical Hartree system

Electronic Journal of Qualitative Theory of Differential Equations
We consider the existence of normalized solutions for a fractional coupled Hartree system, with the upper critical exponent in the sense of the Hardy-Littelwood-Sobolev inequality.
Shengbing Deng, Wenshan Luo
doaj   +1 more source