Positive radial solutions for Dirichlet problems via a Harnack-type inequality


We deal with the existence and localization of positive radial solutions for Dirichlet problems involving \(\phi\)-Laplacian operators in a ball. In particular, \(p\)-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.


Radu Precup
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania

Jorge Rodríguez-López
CITMAga and Departamento de Estatística, Análise Matemática e Optimización, Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago, Spain


compression–expansion, Dirichlet problem, fixed point index, Harnack-type inequality, mean cur-vature operator, Positive radial solution

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R. Precup, J. Rodríguez-López, Positive radial solutions for Dirichlet problems via a Harnack-type inequality, Mathematical Methods in the Applied Sciences, 46 (2023) no. 2, pp. 2972-2985, https://doi.org/10.1002/mma.8682


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