A nonexistence result for a nonlinear equation involving critical Sobolev exponent

An existence result for nonlinear elliptic problems involving critical Sobolev exponent

In this paper we consider the following problem: where Q c Rn is a bounded domain and We prove the existence of a nontrivial solution of (1) for any ~, > 0, RESUME. Soient Q un sous-ensemble ouvert borne de Rn et À un nombre positif, le but de cette note c’est de montrer que le probleme suivant : admet, au moins, une solution non triviale, si r~ > 4. Work supported by G. N. A. F. A. o...

Nonexistence results for a class of nonlinear elliptic equations involving critical Sobolev exponents

A Non-Linear problem involving critical Sobolev exponent

We study the non-linear minimization problem on H 0 (Ω) ⊂ L q with q = 2n n−2 : inf ‖u‖ Lq =1 ∫ Ω (1 + |x| |u|)|∇u|. We show that minimizers exist only in the range β < kn/q which corresponds to a dominant nonlinear term. On the contrary, the linear influence for β ≥ kn/q prevents their existence.

The Solvability of Concave-Convex Quasilinear Elliptic Systems Involving $p$-Laplacian and Critical Sobolev Exponent

In this work, we study the existence of non-trivial multiple solutions for a class of quasilinear elliptic systems equipped with concave-convex nonlinearities and critical growth terms in bounded domains. By using the variational method, especially Nehari manifold and Palais-Smale condition, we prove the existence and multiplicity results of positive solutions.

Fast Diffusion Equation with Critical Sobolev Exponent in a Ball