Multiple positive solutions for nonlinear periodic problems
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. © 2010 Elsevier Ltd. All rights reserved.
Morse theory, Mountain pass theorem, Periodic scalar p-Laplacian
Hu, Shouchuan, and Nikolas S. Papageorgiou. "Multiple positive solutions for nonlinear periodic problems." Nonlinear Analysis: Theory, Methods & Applications 73, no. 12 (2010): 3675-3687.
Nonlinear Analysis, Theory, Methods and Applications