Multiple solutions for some nonlinear Schrödinger equations with indefinite linear part (Q878469)

The author considers a class of nonlinear Schrödinger equations with indefinite linear part in \(\mathbb{R}^N\): \(-\Delta u+V_\lambda (x) u=f(x,u),\;u\in H^1(\mathbb{R}^N).\) It is proved that the corresponding problem has at least three nontrivial solutions. The results are primarily an application of a linking theorem, due to \textit{M. Willem} [Minimax Theorems, Birkhäuser Boston (1996; Zbl 0856.49001)], and a (\(\nabla\))-Theorem, initiated by \textit{A. Marino} and \textit{C. Saccon} [Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 25, No.~3--4, 631--665 (1997; Zbl 1033.35026)]).