Nonlinear nonhomogeneous boundary value problems with competition phenomena

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

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.

• Jezik: Angleški jezik
• Ključne besede: nonlinear nonhomogeneous differential operator, nonlinear boundary condition, nonlinear regularity theory, nonlinear maximum principle, critical groups
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: PEF - Pedagoška fakulteta; FMF - Fakulteta za matematiko in fiziko
• Leto izida: 2019
• Št. strani: Str. 251-298
• Številčenje: Vol. 80, iss. 1
• PID: 20.500.12556/RUL-108776
• UDK: 517.956.2
• ISSN pri članku: 0095-4616
• DOI: 10.1007/s00245-017-9465-6
• COBISS.SI-ID: 18194265
• Datum objave v RUL: 23.07.2019

Gradivo je del revije

• Naslov: Applied mathematics and optimization
• Skrajšan naslov: Appl. math. optim.
• Založnik: Springer.
• ISSN: 0095-4616
• COBISS.SI-ID: 24984064