Nikolaos Socrates Papageorgiou (Author), Vicenţiu Rǎdulescu (Author), Dušan Repovš (Author)

Abstract

We consider a nonlinear boundary value problem driven by a nonhomogeneous differential operator. The problem exhibits competing nonlinearities with a superlinear (convex) contribution coming from the reaction term and a sublinear (concave) contribution coming from the parametric boundary (source) term. We show that for all small parameter values ▫$\lambda > 0$▫, the problem has at least five nontrivial smooth solutions, four of constant sign and one nodal. We also produce extremal constant sign solutions and determine their monotonicity and continuity properties as the parameter ▫$\lambda > 0$▫ varies. In the semilinear case we produce a sixth nontrivial solution but without any sign information. Our approach uses variational methods together with truncation and perturbation techniques, and Morse theory.

Keywords

nonlinear nonhomogeneous differential operator;nonlinear boundary condition;nonlinear regularity theory;nonlinear maximum principle;critical groups;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UL FMF - Faculty of Mathematics and Physics
UDC: 517.956.2
COBISS: 18194265 Link will open in a new window
ISSN: 0095-4616
Views: 603
Downloads: 347
Average score: 0 (0 votes)
Metadata: JSON JSON-RDF JSON-LD TURTLE N-TRIPLES XML RDFA MICRODATA DC-XML DC-RDF RDF

Other data

Type (COBISS): Article
Pages: str. 251-298
Volume: ǂVol. ǂ80
Issue: ǂiss. ǂ1
Chronology: Aug. 2019
DOI: 10.1007/s00245-017-9465-6
ID: 11193169