Solutions for a nonhomogeneous nonlinear Schrödinger equation with double power nonlinearity. (English) Zbl 1212.35114

Ghimenti, M.; Micheletti, A. M.

Differ. Integral Equ. 20, No. 10, 1131-1152 (2007).

Summary: We consider the problem \(-\Delta u+V(x)u=f'(u)+g(x)\) in \(\mathbb R^N\), under the assumption \(\lim _{x\to \infty }V(x)=0\), and with the nonlinear term \(f\) with a double power behavior. We prove the existence of two solutions when \(g\) is sufficiently small and \(V<0\).

MSC:

35J60	Nonlinear elliptic equations
35D30	Weak solutions to PDEs
35J20	Variational methods for second-order elliptic equations

Keywords:

nonlinear Schrödinger equation; double power; nonlinearity; existence