Nonlinear nonhomogeneous boundary value problems with competition phenomena
ID Papageorgiou, Nikolaos S. (Author), ID Rǎdulescu, Vicenţiu (Author), ID Repovš, Dušan (Author)

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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
Work type:Article
Typology:1.01 - Original Scientific Article
Organization:PEF - Faculty of Education
FMF - Faculty of Mathematics and Physics
Number of pages:Str. 251-298
Numbering:Vol. 80, iss. 1
PID:20.500.12556/RUL-108776 This link opens in a new window
ISSN on article:0095-4616
DOI:10.1007/s00245-017-9465-6 This link opens in a new window
COBISS.SI-ID:18194265 This link opens in a new window
Publication date in RUL:23.07.2019
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Title:Applied mathematics and optimization
Shortened title:Appl. math. optim.
COBISS.SI-ID:24984064 This link opens in a new window

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