Antisymmetric solutions for a class of quasilinear defocusing Schrödinger equations - Soares Gamboa Janette (Electronic journal of qualitative theory of differential equations, 2020)
In this paper we consider the existence of antisymmetric solutions for the quasilinear defocusing Schrödinger equation in H1 (RN): −∆u + k 2 u∆u 2 + V(x)u = g(u), where N ≥ 3, V(x) is a positive continuous potential, g(u) is of subcritical growth and k is a non-negative parameter. By considering a minimizing problem restricted on a partial Nehari manifold, we prove the existence of antisymmetric solutions via a deformation lemma.