Soliton solutions for quasilinear Schrödinger equations, I

Abstract

Abstract. For a class of quasilinear Schrödinger equations we establish the existence of ground states of soliton type solutions by a minimization argument.

Multibump solutions for quasilinear elliptic equations with critical growth

“…2,9,12,18,23,25,26,[29][30][31], and 35 and references therein). These type equations have been considered in models from mathematical physics (e.g., Refs.…”

Positive solution for quasilinear Schrödinger equations with a parameter

“…(1.2) was used for the superfluid film equation in plasma physics [5]. Several methods can be used to solve this case, e.g., the existence of positive solutions, negative solutions and sequence of high energy solutions has been prove in [10,15] by using a perturbation method; the problem is transformed to a semilinear one in [1,2,3,8,13,19] by a dual approach; Nehari method is used to get the existence of ground state solutions in [11,16].…”

Existence results for quasilinear Schrödinger equations with a general nonlinearity

“…Indeed, during the last twenty years, a considerable amount of research is devoted to studying (1.1) and related problems. Many existence and multiplicity results were proved by using different approaches, such as minimizations [24,29], change of variables [8,11,22], Nehari method [23] and perturbation method [25,27]. In [22], by a suitable change of variables, problem (1.1) was reduced to a semilinear elliptic equation and existence results were proved under four different types of potentials in an Orlicz space framework.…”