The reaction–diffusion equation with Lewis function and critical Sobolev exponent

Fast Diffusion Equation with Critical Sobolev Exponent in a Ball

Ja n 20 04 Schrödinger equation with critical Sobolev exponent

p-Laplacian problems with critical Sobolev exponent

We use variational methods to study the asymptotic behavior of solutions of p-Laplacian problems with nearly subcritical nonlinearity in general, possibly non-smooth, bounded domains.

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.

Problem with critical Sobolev exponent and with weight

We consider the problem: −div(p∇u) = u + λu, u > 0 in Ω, u = 0 on ∂Ω. Where Ω is a bounded domain in IR, n ≥ 3, p : Ω̄ −→ IR is a given positive weight such that p ∈ H(Ω) ∩ C(Ω̄), λ is a real constant and q = 2n n−2 . We study the effect of the behavior of p near its minima and the impact of the geometry of domain on the existence of solutions for the above problem.