Electron. J. Differential Equations, Vol. 2021 (2021), No. 12, pp. 1-24.

Multiple solutions for semilinear Robin problems with superlinear reaction and no symmetries

Nikolaos S. Papageorgiou, Calogero Vetro, Francesca Vetro

We study a semilinear Robin problem driven by the Laplacian with a parametric superlinear reaction. Using variational tools from the critical point theory with truncation and comparison techniques, critical groups and flow invariance arguments, we show the existence of seven nontrivial smooth solutions, all with sign information and ordered.

Submitted February 15, 2021. Published March 10, 2021.
Math Subject Classifications: 35J20, 35J61.
Key Words: Constant sign and nodal solutions; superlinear reaction; critical point theory; critical groups; flow invariance.

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  Nikolaos S. Papageorgiou
National Technical University
Department of Mathematics, Zografou campus
15780, Athens, Greece
email: npapg@math.ntua.gr
Calogero Vetro
University of Palermo
Department of Mathematics and Computer Science
Via Archirafi 34, 90123
Palermo, Italy
email: calogero.vetro@unipa.it
Francesca Vetro
90123, Palermo, Italy
email: francescavetro80@gmail.com

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