Positive solutions for nonlinear parametric singular Dirichlet problems

• Published in: Bulletin of mathematical sciences Vol. 9; no. 3; pp. 1950011 - 1950011-21
• Main Authors: Papageorgiou, Nikolaos S., Rădulescu, Vicenţiu D., Repovš, Dušan D.
• Format: Journal Article
• Language: English
• Published: World Scientific Publishing Company 01.12.2019; World Scientific Publishing
• Subjects: (p − 1)-linear perturbation; bifurcation-type theorem; nonlinear regularity theory; parametric singular term; strong comparison principle; truncation; uniform nonresonance; nonlinear regularity theory; strong comparison principle; (; linear perturbation; uniform nonresonance; Parametric singular term; bifurcation-type theorem; truncation
• ISSN: 1664-3607; 1664-3615
• DOI: 10.1142/S1664360719500115

We consider a nonlinear parametric Dirichlet problem driven by the p -Laplace differential operator and a reaction which has the competing effects of a parametric singular term and of a Carathéodory perturbation which is ( p − 1 )-linear near + ∞ . The problem is uniformly nonresonant with respect to the principal eigenvalue of ( − Δ p , W 0 1 , p ( Ω ) ) . We look for positive solutions and prove a bifurcation-type theorem describing in an exact way the dependence of the set of positive solutions on the parameter λ > 0 .