Nonlinear nonhomogeneous boundary value problems with competition phenomena

Papageorgiou, Nikolaos S. (author), Rǎdulescu, Vicenţiu (author), Repovš, Dušan (author)

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.

• Language: English
• Keywords: nonlinear nonhomogeneous differential operator, nonlinear boundary condition, nonlinear regularity theory, nonlinear maximum principle, critical groups
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2019
• Number of pages: Str. 251-298
• Numbering: Vol. 80, iss. 1
• PID: 20.500.12556/RUL-108776
• UDC: 517.956.2
• ISSN on article: 0095-4616
• DOI: 10.1007/s00245-017-9465-6
• COBISS.SI-ID: 18194265
• Publication date in RUL: 23.07.2019

Record is a part of a journal

• Title: Applied mathematics and optimization
• Shortened title: Appl. math. optim.
• Publisher: Springer.
• ISSN: 0095-4616
• COBISS.SI-ID: 24984064