Nonlinear nonhomogeneous singular problems

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

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 ▫$\lambda \mapsto u^\ast_\lambda$▫.

• Language: English
• Keywords: singular term, superlinear perturbation, positive solution, nonhomogeneous differential operator, nonlinear regularity, minimal positive solutions, strong comparison principle
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2020
• Number of pages: art. 9 [31 str.]
• Numbering: Vol. 59, iss. 1
• PID: 20.500.12556/RUL-116612
• UDC: 517.956.2
• ISSN on article: 0944-2669
• DOI: 10.1007/s00526-019-1667-0
• COBISS.SI-ID: 18823001
• Publication date in RUL: 29.05.2020

Record is a part of a journal

• Title: Calculus of variations and partial differential equations
• Shortened title: Calc. var. partial differ. equ.
• Publisher: Springer
• ISSN: 0944-2669
• COBISS.SI-ID: 3677529