MR2589665 Sophia Th. KYRITSI and Nikolas S. PAPAGEORGIOU Sophia Th. KYRITSI and Nikolas S. PAPAGEORGIOU Multiple Constant Sign and Nodal Solutions for Superlinear Elliptic Equations Funkcialaj Ekvacioj. Serio Internacia 52 2009 437--473 http://fe.math.kobe-u.ac.jp/FE/FullPapers/52-3/52_437.pdf http://www.ams.org/mathscinet-getitem?mr=MR2589665 We consider semilinear elliptic problems with a superlinear right hand side nonlinearity, which however, need not satisfy the Ambrosetti-Rabinowitz condition. Using a combination of variational methods, with Morse theory (critical groups) and truncation techniques, we prove multiplicity theorems providing precise sign information for the solutions. We show that the problem can have seven and eight solutions, all with prescribed sign. $C$-condition, Mountain pass theorem, Second deformation theorem, Morse theory, Critical groups, Superlinear problems. 35J25, 35J80, 58E05. 52-437 2009 Multiple Constant Sign and Nodal Solutions for Superlinear Elliptic Equations Sophia Th. KYRITSI and Nikolas S. PAPAGEORGIOU Sophia Th. KYRITSI and Nikolas S. PAPAGEORGIOU
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