Perturbed Problems Involving the Square Root of the Laplacian

We prove multiplicity of solutions for perturbed problems involving the square root of the Laplacian A = (-Delta)(1/2). More precisely, we consider the problem { Au = lambda u + f(x,u) + epsilon g(x,u) in Omega u = 0 on partial derivative Omega, where Omega subset of R-N is a bounded domain, epsilon is an element of R, N > 1, f is a subcritical function with asymptotic linear behavior at infinity, and g is a continuous function. We also show the invariance under small perturbations of the number of distinct critical levels of the associated energy functional to the unperturbed problem, in both resonant and non-resonant case.

fractional laplacian; variational methods; multiplicity of solutions; regularity; resonance; theorems

Perturbed Problems Involving the Square Root of the Laplacian Articles