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

Language: English nonlinear nonhomogeneous differential operator, nonlinear boundary condition, nonlinear regularity theory, nonlinear maximum principle, critical groups Article (dk_c) 1.01 - Original Scientific Article PEF - Faculty of Education 2019 Str. 251-298 Vol. 80, iss. 1 517.956.2 0095-4616 10.1007/s00245-017-9465-6 18194265 427 257 (0 votes) Voting is allowed only to logged in users. AddThis uses cookies that require your consent. Edit consent...

## Record is a part of a journal

Title: Applied mathematics and optimization Appl. math. optim. Springer. 0095-4616 24984064