The Choquard Equation with Weighted Terms and Sobolev-Hardy Exponent

On the quasilinear elliptic problem with a critical Hardy–Sobolev exponent and a Hardy term

In the present paper, a quasilinear elliptic problem with a critical Sobolev exponent and a Hardy-type term is considered. By means of a variational method, the existence of nontrivial solutions for the problem is obtained. The result depends crucially on the parameters p, t, s, λ and μ. c © 2007 Elsevier Ltd. All rights reserved. MSC: 35J60; 35B33

Fast Diffusion Equation with Critical Sobolev Exponent in a Ball

Ja n 20 04 Schrödinger equation with critical Sobolev exponent

The Kawahara equation in weighted Sobolev spaces

Abstract The initialand boundary-value problem for the Kawahara equation, a fifthorder KdV type equation, is studied in weighted Sobolev spaces. This functional framework is based on the dual-Petrov–Galerkin algorithm, a numerical method proposed by Shen (2003 SIAM J. Numer. Anal. 41 1595–619) to solve third and higher odd-order partial differential equations. The theory presented here includes...

Multiplicity Results for Equations with Subcritical Hardy-sobolev Exponent and Singularities on a Half-space

We prove some multiplicity results for a class of singular quasilinear elliptic problems involving the critical Hardy-Sobolev exponent and singularities on a half-space.