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Nodal Solutions for Indefinite Robin Problems

  • Michael Filippakis
  • Nikolaos S. PapageorgiouEmail author
Article
  • 95 Downloads

Abstract

We consider a semilinear Robin problem driven by the negative Laplacian plus an indefinite, unbounded potential. The reaction term is a Caratheodory function of arbitrary structure outside an interval \([-c,c]\) (\(c>0\)), odd on \([-c,c]\) and concave near zero. Using a variant of the symmetric mountain pass theorem, together with truncation, perturbation and comparison techniques, we show that the problem has a whole sequence \(\{u_n\}_{n\ge 1}\) of distinct nodal solutions converging to zero in \(C^1({\overline{\Omega }})\).

Keywords

Indefinite potential Robin boundary condition Sequence of nodal solution Regularity theory Strong maximum principle 

Mathematics Subject Classification

35J20 35J60 

Notes

Acknowledgements

The authors wish to thank the referee for his/her remarks.

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2017

Authors and Affiliations

  1. 1.Department of Digital SystemsUniversity of PiraeusPiraeusGreece
  2. 2.Department of MathematicsNational Technical UniversityAthensGreece

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