Behaviors of solutions to a scalar-field equation involving the critical Sobolev exponent with the Robin condition

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

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

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. The main tools adopted in our proofs are the concentration compactness principle and Nehari manifold.

Bifurcation of Positive Solutions for a Semilinear Equation with Critical Sobolev Exponent

In this note we consider bifurcation of positive solutions to the semilinear elliptic boundary-value problem with critical Sobolev exponent −∆u = λu− αu + u −1, u > 0, in Ω, u = 0, on ∂Ω. where Ω ⊂ Rn, n ≥ 3 is a bounded C2-domain λ > λ1, 1 < p < 2∗ − 1 = n+2 n−2 and α > 0 is a bifurcation parameter. Brezis and Nirenberg [2] showed that a lower order (non-negative) perturbation can contribute t...

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.