Abstract.
By using a Liapunov-Schmidt reduction we prove an existence result for the nonlinear Schrödinger equation \(-h^2\Delta u+V(x)u=f(x,u)\) in \(R^N\) where \(f(x,u)\) satisfies suitable assumptions. We also provide a necessary condition for the existence of solutions.
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Received June 7, 1999 / in final form November 10, 1999 / Published online July 20, 2000
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Grossi, M. Some results on a class of nonliner Schrödinger equations. Math Z 235, 687–705 (2000). https://doi.org/10.1007/s002090000158
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DOI: https://doi.org/10.1007/s002090000158