Multiple positive solutions for nonlinear periodic problems |
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| Authors: | Shouchuan Hu Nikolas S Papageorgiou |
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| Institution: | a College of Mathematics, Shandong Normal University, Jinan, Shandong, Chinab Department of Mathematics, Missouri State University, Springfield, MO 65804, USAc Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece |
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| Abstract: | 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. |
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| Keywords: | 34B15 34B18 34C25 58E05 |
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