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Variational principle for nonlinear Schrödinger equation with high nonlinearity. (English) Zbl 1161.58307

Summary: It is well-known that the Schrödinger equation plays an important role in physics and applied mathematics as well. Variational formulations have been one of the hottest topics. This paper suggests a simple but effective method called the semi-inverse method proposed by Ji-Huan He to construct a variational principle for the nonlinear Schrödinger equation with high nonlinearity.

MSC:

58E30 Variational principles in infinite-dimensional spaces
35A15 Variational methods applied to PDEs
34G20 Nonlinear differential equations in abstract spaces
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