Zeitschrift für Analysis und ihre Anwendungen


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Volume 36, Issue 2, 2017, pp. 209–238
DOI: 10.4171/ZAA/1586

Published online: 2017-03-29

Nonlinear Dirichlet Problems with no Growth Restriction on the Reaction

Leszek Gasiński[1], Liliana Klimczak[2] and Nikolaos S. Papageorgiou[3]

(1) Jagiellonian University, Kraków, Poland
(2) Jagiellonian University, Kraków, Poland
(3) National Technical University of Athens, Greece

We consider nonlinear Dirichlet problems driven by the sum of a $p$-Laplacian and a Laplacian and with a Carathéodory reaction which does not satisfy any global growth condition. Instead we assume that it has constant sign $z$-dependent zeros. Using variational methods, truncation techniques and Morse theory, we prove multiplicity theorems providing sign information for all the solutions.

Keywords: Nonlinear regularity, nonlinear maximum principle, constant sign and nodal solutions, $(p, 2)$-equation, critical groups

Gasiński Leszek, Klimczak Liliana, Papageorgiou Nikolaos: Nonlinear Dirichlet Problems with no Growth Restriction on the Reaction. Z. Anal. Anwend. 36 (2017), 209-238. doi: 10.4171/ZAA/1586