A parameterized quasilinear Schrödinger equation with indefinite potentials. (March 2020) - Giacomoni, Jacques; Santos, Carlos Alberto; Yang, Minbo; Zhou, Jiazheng
Abstract: In this paper we consider the existence of solutions for the quasilinear Schrödinger equation − Δ u − k Δ [ ( 1 + u 2 ) 1 ∕ 2 ] u 2 ( 1 + u 2 ) 1 ∕ 2 + V ( x ) u = g ( u ) in H 1 ( R N ) ∩ L l o c ∞ ( R N ), where N ≥ 3, V is a continuous potential allowed to be indefinite, g is a subcritical growth function, and k is a real parameter. By using local linking arguments and computing the critical groups of the energy functional, we obtain the existence of nontrivial solution for the equation.