On Schrödinger equation with periodic potential and critical Sobolev exponent

Ja n 20 04 Schrödinger equation with critical Sobolev exponent

Fast Diffusion Equation with Critical Sobolev Exponent in a Ball

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.

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.

On a Schrödinger equation with periodic potential involving critical growth

The main purpose of this paper is to establish the existence of a solution of the semilinear Schrödinger equation −∆u + V (x)u = f(u), in R where V is a 1-periodic functions with respect to x, 0 lies in a gap of the spectrum of −∆ + V , and f(s) behaves like ± exp(αs) when s → ±∞.