Multiple positive solutions for a class of p-superlinear elliptic problems

作者：Kyritsi Sophia Th; Papageorgiou Nikolaos S^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2010, 72(6): 3069-3079.

DOI：10.1016/j.na.2009.11.046

• p-Laplacian
• p-superlinear term
• p-linear nonlinearity
• Truncations
• Critical point theory
• Morse theory
• Positive solutions
• Constant sign solutions

We study nonlinear elliptic Dirichlet problems driven by the p-Laplacian and with a nonlinearity which consists of a p-superlinear term perturbed by a p-linear one. Using critical point theory, coupled with suitable truncation techniques, we show that the problem has two positive smooth solutions. When the conditions are symmetric in the two semiaxes, we have four nontrivial smooth solutions of constant sign. Finally for the semilinear problem, using Morse theory, we produce a fifth nontrivial smooth solution.

• 出版日期2010-3-15
• 单位中国人民解放军海军大连舰艇学院