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Topological Methods in Nonlinear Analysis

Multiple nodal solutions for semilinear Robin problems with indefinite linear part and concave terms
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Multiple nodal solutions for semilinear Robin problems with indefinite linear part and concave terms

Authors

  • Nikolaos S. Papageorgiou
  • Calogero Vetro
  • Francesca Vetro

Keywords

Indefinite potential, nodal solutions, extremal constant sign solutions, regularity theory, concave term

Abstract

We consider a semilinear Robin problem driven by Laplacian plus an indefinite and unbounded potential. The reaction function contains a concave term and a perturbation of arbitrary growth. Using a variant of the symmetric mountain pass theorem, we show the existence of smooth nodal solutions which converge to zero in $C^1(\overline{\Omega})$. If the coefficient of the concave term is sign changing, then again we produce a sequence of smooth solutions converging to zero in $C^1(\overline{\Omega})$, but we cannot claim that they are nodal.

References

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C. Yu and I. Yongqing, Infinitely many solutions for a semilinear elliptic equation with sign-changing potential, Bound. Value Probl. 2009 (2009), Article ID 532546, 7 pp.

Q. Zhang and C. Liu, Multiple solutions for a class of semilinear elliptic equations with general potentials, Nonlinear Anal. 75 (2012), 5473–5481.

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Published

2017-08-19

How to Cite

1.
PAPAGEORGIOU, Nikolaos S., VETRO, Calogero and VETRO, Francesca. Multiple nodal solutions for semilinear Robin problems with indefinite linear part and concave terms. Topological Methods in Nonlinear Analysis. Online. 19 August 2017. Vol. 50, no. 1, pp. 269 - 286. [Accessed 5 July 2025].
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Vol 50, No 1 (September 2017)

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