Nodal Solutions for Indefinite Robin Problems

  • Michael Filippakis
  • Nikolaos S. PapageorgiouEmail author


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 \(C^1({\overline{\Omega }})\).


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

Mathematics Subject Classification

35J20 35J60 



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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