Nikolaos S. Papageorgiou, Calogero Vetro, Francesca Vetro
We consider a parametric Neumann problem driven by a nonlinear nonhomogeneous differential operator plus an indefinite potential term. The reaction term is superlinear but does not satisfy the Ambrosetti-Rabinowitz condition. First we prove a bifurcation-type result describing in a precise way the dependence of the set of positive solutions on the parameter . We also show the existence of a smallest positive solution. Similar results hold for the negative solutions and in this case we have a biggest negative solution. Finally using the extremal constant sign solutions we produce a smooth nodal solution.
Submitted February 11, 2019. Published January 24, 2020.
Math Subject Classifications: 35J20, 35J60, 58E05.
Key Words: Nonlinear nonhomogeneous differential operator; nonlinear regularity theory; nonlinear maximum principle; strong comparison; bifurcation-type theorem; nodal solution; critical group.
Show me the PDF file (392 KB), TEX file for this article.
| Nikolaos S. Papageorgiou |
National Technical University
Department of Mathematics, Zografou campus
15780, Athens, Greece
| Calogero Vetro |
University of Palermo
Department of Mathematics and Computer Science
Via Archirafi 34, 90123, Palermo, Italy
| Francesca Vetro |
Nonlinear Analysis Research Group
Faculty of Mathematics and Statistics
Ton Duc Thang University
Ho Chi Minh City, Vietnam
Return to the EJDE web page