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Three nontrivial solutions for periodic problems with the \(p\)-Laplacian and a \(p\)-superlinear nonlinearity. (English) Zbl 1172.34011

The paper is concerned with the study of a nonlinear periodic problem driven by the scalar \(p\)-Laplacian and a \(p\)-superlinear growth near \(\pm\infty \). Using a combination of minimax methods based on critical point theory, together with truncation techniques and Morse theoretic arguments, the authors show that this problem has at least three nontrivial solutions, two of which have constant sign.

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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