A multiplicity theorem for p-superlinear p-Laplacian equations using critical groups and morse theory

作者：Kyritsi Sophia Th; O'Regan Donal; Papageorgiou Nikolaos S^*

来源：Monatshefte fur Mathematik, 2011, 163(4): 471-491.

DOI：10.1007/s00605-010-0201-4

• p-Superlinear nonlinearity
• C-condition
• Indefinite Euler function
• Mountain pass theorem
• Critical groups
• Morse theory

We study a nonlinear elliptic equation driven by the Dirichlet p-Laplacian and with a Carath,odory nonlinearity. We assume that the nonlinearity exhibits a p-superlinear growth near infinity but need not satisfy the Ambrosetti-Rabinowitz condition. Using truncation techniques, minimax methods and Morse theory, we show that the problem admits at least three nontrivial solutions, two of which have constant sign (one positive, the other negative).

• 出版日期2011-8
• 单位中国人民解放军海军大连舰艇学院