Revista Matemática Iberoamericana

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Volume 33, Issue 1, 2017, pp. 251–289
DOI: 10.4171/RMI/936

Published online: 2017-02-22

Multiplicity theorems for nonlinear nonhomogeneous Robin problems

Nikolaos S. Papageorgiou[1] and Vicenţiu D. Rădulescu[2]

(1) National Technical University of Athens, Greece
(2) King Abdulaziz University, Jeddah, Saudi Arabia and University of Craiova, Romania

We study a nonlinear Robin boundary value driven by a nonhomogeneous differential operator with a Carathéodory reaction and we look for multiple nontrivial solutions with sign information. We prove four such multiplicity theorems producing three nontrivial solutions, for resonant problems and for problems in which no global growth restriction is assumed on the reaction. Also, in the semilinear case, we show that we can have four nontrivial solutions, by producing a second nodal solution.

Keywords: Nonhomogeneous differential operator, Robin boundary condition, resonance, nonlinear regularity, nonlinear maximum principle, critical groups, nodal solution

Papageorgiou Nikolaos, Rădulescu Vicenţiu: Multiplicity theorems for nonlinear nonhomogeneous Robin problems. Rev. Mat. Iberoamericana 33 (2017), 251-289. doi: 10.4171/RMI/936