Solutions for quasilinear Schrödinger equations via the Nehari method. (English) Zbl 1140.35399
The authors deal with the following quasilinear Schrödinger type equation
\[ -\Delta_xu+V(x)u-\tfrac 12(\Delta_x(| u|^2))u= \lambda| u|^{p-1}u \quad\text{ in }\mathbb{R}^N,\;\lambda>0.\tag{1} \] Under some natural assumptions on \(V(x)\) and \(p\in\mathbb{R}\) the authors prove the existence of both one-sign and nodal ground states solition type solutions for (1). To this end they use the Nehari method.
\[ -\Delta_xu+V(x)u-\tfrac 12(\Delta_x(| u|^2))u= \lambda| u|^{p-1}u \quad\text{ in }\mathbb{R}^N,\;\lambda>0.\tag{1} \] Under some natural assumptions on \(V(x)\) and \(p\in\mathbb{R}\) the authors prove the existence of both one-sign and nodal ground states solition type solutions for (1). To this end they use the Nehari method.
Reviewer: Messoud A. Efendiev (München)
MSC:
| 35J10 | Schrödinger operator, Schrödinger equation |
| 35J20 | Variational methods for second-order elliptic equations |
| 35J60 | Nonlinear elliptic equations |
Keywords:
standig waves; quasilinear Schrödinger equation; one-sign and nodal solutions; Nehari methodReferences:
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