Nonlinear resonant periodic problems with concave terms |
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Authors: | Sergiu Aizicovici |
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Institution: | a Department of Mathematics, Ohio University, Athens, OH 45701, USA b Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece c Department of Mathematics, University of Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal |
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Abstract: | We consider a nonlinear periodic problem, driven by the scalar p-Laplacian with a concave term and a Caratheodory perturbation. We assume that this perturbation f(t,x) is (p−1)-linear at ±∞, and resonance can occur with respect to an eigenvalue λm+1, m?2, of the negative periodic scalar p-Laplacian. Using a combination of variational techniques, based on the critical point theory, with Morse theory, we establish the existence of at least three nontrivial solutions. Useful in our considerations is an alternative minimax characterization of λ1>0 (the first nonzero eigenvalue) that we prove in this work. |
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Keywords: | Critical groups Ekeland variational principle C-condition Concave term Strong deformation retract Homotopy equivalent Contractible space |
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