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Seven solutions with sign information for sublinear equations with unbounded and indefinite potential and no symmetries

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Abstract

We consider a semilinear Dirichlet problem with an unbounded and indefinite potential and a superlinear reaction which need not satisfy the usual, in such cases, Ambrosetti-Rabinowitz condition. Using a combination of variational methods (critical point theory) with truncation and comparison techniques, with Morse theory and with flow invariance arguments, we show that the problem has at least seven nontrivial smooth solutions and provide sign information for all of them.

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Authors and Affiliations

  1. Department of Mathematics, National Technical University, Zografou Campus, Athens, 15780, Greece

    Nikolaos S. Papageorgiou

  2. Department of Industrial Engineering and Mathematical Sciences, Polytechnic University of Marche, Brecce Bianche, 60131, Ancona, Italy

    Francesca Papalini

Authors
  1. Nikolaos S. Papageorgiou
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  2. Francesca Papalini
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Correspondence to Nikolaos S. Papageorgiou.

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Papageorgiou, N.S., Papalini, F. Seven solutions with sign information for sublinear equations with unbounded and indefinite potential and no symmetries. Isr. J. Math. 201, 761–796 (2014). https://doi.org/10.1007/s11856-014-1050-y

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  • DOI: https://doi.org/10.1007/s11856-014-1050-y

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