Weak Linking Theorems and Schrödinger Equations with Critical Sobolev Exponent

Ja n 20 04 Schrödinger equation with critical Sobolev exponent

Non-homogeneous semilinear elliptic equations involving critical Sobolev exponent

where λ > 0 is a parameter, κ ∈ R is a constant, p = (N + 2)/(N − 2) is the critical Sobolev exponent, and f(x) is a non-homogeneous perturbation satisfying f ∈ H−1(Ω) and f ≥ 0, f ≡ 0 in Ω. Let κ1 be the first eigenvalue of −Δ with zero Dirichlet condition on Ω. Since (1.1)λ has no positive solution if κ ≤ −κ1 (see Remark 1 below), we will consider the case κ > −κ1. Let us recall the results f...

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.

Elliptic Equations with Critical Exponent

where As3 is the Laplace-Beltrami operator on B' . Let 0* C (0, 7r) be the radius o r B ' , i.e., the geodesic distance of the North pole to OBq The values 0 < 0* < 7r/2 correspond to a spherical cap contained in the Northern hemisphere, 0* -7r/2 corresponds to B ~ being the Northern hemisphere and the values rr/2 < 0* < ~c correspond to a spherical cap which covers the Northern hemisphere. Fin...

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.