Kyoto Journal of Mathematics

Multiplicity of solutions for Neumann problems resonant at any eigenvalue

Leszek Gasiński and Nikolaos S. Papageorgiou

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We consider a semilinear Neumann problem with a reaction which is resonant both at ± and at zero with respect to any eigenvalue, possibly the same one. Using the reduction method and Morse theory, we show that the problem has at least two nontrivial smooth solutions.

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Kyoto J. Math., Volume 54, Number 2 (2014), 259-269.

First available in Project Euclid: 2 June 2014

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Zentralblatt MATH identifier

Primary: 35J20: Variational methods for second-order elliptic equations
Secondary: 35J60: Nonlinear elliptic equations 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)


Gasiński, Leszek; Papageorgiou, Nikolaos S. Multiplicity of solutions for Neumann problems resonant at any eigenvalue. Kyoto J. Math. 54 (2014), no. 2, 259--269. doi:10.1215/21562261-2642386.

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