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Multiple constant sign and nodal solutions for superlinear elliptic equations. (English) Zbl 1190.35094

The existence of multiple solutions for semilinear elliptic equations with homogeneous Dirichlet boundary condition is proven in the case where the nonlinear terms have a superlinear growth, but they do not necessarily satisfy the Ambrosetti-Rabinowitz condition. For the obtained solutions, the authors are able to give precise information about the sign of the solutions. In this respect, constant sign and sign changing solutions are found. The approach relies on variational methods, sub-supersolutions, truncation techniques and Morse theory.

MSC:

35J61 Semilinear elliptic equations
35J20 Variational methods for second-order elliptic equations
35J25 Boundary value problems for second-order elliptic equations
35B09 Positive solutions to PDEs
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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