We consider nonlinear nonhomogeneous Dirichlet problems driven by the sum of a p -Laplacian and a Laplacian. The hypotheses on the reaction term incorporate problems resonant at both ±∞ and zero. We consider both cases p >2 and 1< p <2 (singular case) and we prove four multiplicity theorems producing three or four nontrivial solutions. For the case p >2 we provide precise sign information for all the solutions. Our approach uses critical point theory, truncation and comparison techniques, Morse theory and the Lyapunoff-Schmidt reduction method.
Applied Mathematics and Optimization – Springer Journals
Published: Jun 1, 2014
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