Kyritsi, Sophia Th.; Papageorgiou, Nikolaos S. Multiple constant sign and nodal solutions for superlinear elliptic equations. (English) Zbl 1190.35094 Funkc. Ekvacioj, Ser. Int. 52, No. 3, 437-473 (2009). 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. Reviewer: Dumitru Motreanu (Perpignan) 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 Keywords:semilinear elliptic equations; Dirichlet problems; multiple solutions; superlinear growth; sign information; critical point; critical groups; Morse theory PDFBibTeX XMLCite \textit{S. Th. Kyritsi} and \textit{N. S. Papageorgiou}, Funkc. Ekvacioj, Ser. Int. 52, No. 3, 437--473 (2009; Zbl 1190.35094) Full Text: DOI