Nonlinear nonhomogeneous singular problems

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

We consider a nonlinear Dirichlet problem driven by a nonhomogeneous differential operator with a growth of order ▫$(p-1)$▫ near ▫$+\infty$▫ and with a reaction which has the competing effects of a parametric singular term and a ▫$(p-1)$▫-superlinear perturbation which does not satisfy the usual Ambrosetti-Rabinowitz condition. Using variational tools, together with suitable truncation and strong comparison techniques, we prove a "bifurcation-type" theorem that describes the set of positive solutions as the parameter ▫$\lambda$▫ moves on the positive semiaxis. We also show that for every ▫$\lambda > 0$▫, the problem has a smallest positive solution ▫$u^\ast_\lambda$▫ and we demonstrate the monotonicity and continuity properties of the map ▫$\lambda \mapsto u^\ast_\lambda$▫.

• Jezik: Angleški jezik
• Ključne besede: singular term, superlinear perturbation, positive solution, nonhomogeneous differential operator, nonlinear regularity, minimal positive solutions, strong comparison principle
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: PEF - Pedagoška fakulteta; FMF - Fakulteta za matematiko in fiziko
• Leto izida: 2020
• Št. strani: art. 9 [31 str.]
• Številčenje: Vol. 59, iss. 1
• PID: 20.500.12556/RUL-116612
• UDK: 517.956.2
• ISSN pri članku: 0944-2669
• DOI: 10.1007/s00526-019-1667-0
• COBISS.SI-ID: 18823001
• Datum objave v RUL: 29.05.2020

Gradivo je del revije

• Naslov: Calculus of variations and partial differential equations
• Skrajšan naslov: Calc. var. partial differ. equ.
• Založnik: Springer
• ISSN: 0944-2669
• COBISS.SI-ID: 3677529