Positive radial solutions for Dirichlet problems via a Harnack‐type inequality. (2nd September 2022)

• Record Type: Journal Article
• Authors: Precup, Radu; Rodríguez‐López, Jorge
• Is Part Of: Mathematical methods in the applied sciences. Volume 46:Number 2(2023)
• Page Start: 2972
• Page End: 2985
• Publication Date: 2022-09-02
• Subjects: compression–expansion -- Dirichlet problem -- fixed point index -- Harnack‐type inequality -- mean curvature operator -- Positive radial solution; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.8682
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : We deal with the existence and localization of positive radial solutions for Dirichlet problems involving ϕ $$ \phi $$ ‐Laplacian operators in a ball. In particular, p $$ p $$ ‐Laplacian and Minkowski‐curvature equations are considered. Our approach relies on fixed point index techniques, which work thanks to a Harnack‐type inequality in terms of a seminorm. As a consequence of the localization result, it is also derived the existence of several (even infinitely many) positive solutions.