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Variant fountain theorems and their applications. (English) Zbl 0976.35026
Summary: We establish some variant fountain theorems without (PS)-type assumption. The abstract results will be used to study the symmetric nonlinear Schrödinger equations and Dirichlet boundary value problems. Under no Ambrosetti-Rabinowitz’s superquadraticity condition, we obtain infinitely many large energy and small negative energy solutions, respectively.

MSC:
35J65 Nonlinear boundary value problems for linear elliptic equations
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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