Nonlinear Robin problems with general potential and crossing reaction

  • Nikolaos S. Papageorgiou

    National Technical University of Athens, Greece
  • Andrea Scapellato

    Università degli Studi di Catania, Italy
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Abstract

We consider a nonlinear Robin problem driven by the -Laplacian plus and indefinite potential. The reaction is parametric and exhibits an asymmetric behavior as . Using variational tools together with truncation, perturbation and comparison techniques and critical groups, we show that for all small values of the parameter , the problem admits at least four nontrivial smooth solutions, three with fixed sign and the fourth nodal. By introducing a local symmetry condition on the reaction, we show that we can have a whole sequence of distinct nodal solutions converging to zero in .

Cite this article

Nikolaos S. Papageorgiou, Andrea Scapellato, Nonlinear Robin problems with general potential and crossing reaction. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 30 (2019), no. 1, pp. 1–29

DOI 10.4171/RLM/833