On the Schrödinger equation involving a critical Sobolev exponent and magnetic field - Chabrowski, Jan; Szulkin, Andrzej (Topological Methods in Nonlinear Analysis, 2005)
We consider the semilinear Schrödinger equation -Δ_A u+V(x)u =Q(x)|u|^2^*-2u. Assuming that V changes sign, we establish the existence of a solution u e 0 in the Sobolev space H_A,V^+^1(). The solution is obtained by a min-max type argument based on a topological linking. We also establish certain regularity properties of solutions for a rather general class of equations involving the operator -Δ_A.