Low and high energy solutions of oscillatory non-autonomous Schrodinger equations with magnetic field

摘要

We are concerned with the mathematical and asymptotic analysis of solutions to the following nonlinear problem{-Delta(A)u = lambda beta(x)vertical bar u vertical bar(q)u + f(vertical bar u vertical bar)u in Omega,u = 0 on partial derivative Omega,where Delta(A)u is the magnetic Laplace operator, Omega subset of R-N is a smooth bounded domain, A : Omega bar right arrow R-N is the magnetic potential, u : Omega bar right arrow C,lambda is a real parameter, beta is an element of L-infinity (Omega, R) is an indefinite potential, q is nonnegative, and f : [0, +infinity) bar right arrow R is a reaction that oscillates either in a neighborhood of the origin or at infinity. We analyze two distinct cases, in close relationship with the oscillatory growth of the reaction. Additionally, we give asymptotic estimates for the norm of the solutions in related function spaces.