Three nontrivial solutions for periodic problems with the $p$-Laplacian and a $p$-superlinear nonlinearity
Leszek Gasiński - Jagiellonian University, Institute of Computer Science, ul. Nawojki 11, 30072 Kraków, Poland (email)
Abstract: We consider a nonlinear periodic problem driven by the scalar $p$-Laplacian and a nonlinearity that exhibits a $p$-superlinear growth near $\pm\infty$, but need not satisfy the Ambrosetti-Rabinowitz condition. Using minimax methods, truncations techniques and Morse theory, we show that the problem has at least three nontrivial solutions, two of which are of fixed sign.
Keywords: Scalar p-Laplacian, mountain pass theorem, critical groups, Morse
theory, Poincaré-Hopf formula.
Received: May 2008; Revised: October 2008; Available Online: March 2009.
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