Multiple positive solutions for nonlinear periodic problems

作者：Hu, Shouchuan^*; Papageorgiou, Nikolas S.

来源：Nonlinear Analysis-Theory Methods & Applications, 2010, 73(12): 3675-3687.

DOI：10.1016/j.na.2010.06.056

• Periodic scalar p-Laplacian
• Mountain pass theorem
• Morse theory

We consider a nonlinear periodic equation driven by the scalar p-Laplacian and with a Caratheodory asymptotically (p - 1)-linear nonlinearity. Using variational methods coupled with suitable truncation techniques, we show that the problem has at least two positive solutions. For the semilinear case (p = 2), using Morse theory we show that the problem has three distinct positive solutions.

• 出版日期2010-12-15
• 单位山东师范大学