On the localization and numerical computation of positive radial solutions for φ-Laplace equations in the annulus

Abstract


The paper deals with the existence and localization of positive radial solutions for stationary partial differential equations involving a general ϕ-Laplace operator in the annulus. Three sets of boundary conditions are considered: Dirichlet–Neumann, Neumann–Dirichlet and Dirichlet–Dirichlet. The results are based on the homotopy version of Krasnosel’skiıs fixed point theorem and Harnack type inequalities, first established for each one of the boundary conditions. As a consequence, the problem of multiple solutions is solved in a natural way. Numerical experiments confirming the theory, one for each of the three sets of boundary conditions, are performed by using the MATLAB object-oriented package Chebfun.

Authors

Jorge Rodríguez-López
CITMAga & Departamento de Estatística, Análise Matemática e Optimización, Universidade de
Santiago de Compostela, 15782, Facultade de Matemáticas, Campus Vida, Santiago, Spain

Radu Precup
Faculty of Mathematics and Computer Science and Institute of Advanced Studies in Science and Technology, Babes-Bolyai University, Cluj-Napoca, Romania
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

Călin-Ioan Gheorghiu
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

Keywords

ϕ-Laplace operator; radial solution; positive solution; fixed point index; Harnack type inequality; numerical solution.

Paper coordinates

J. Rodriguez-Lopez, R. Precup, C.-I. Gheorghiu, On the localization and numerical computation of positive radial solutions for φ-Laplace equations in the annulus, Electronic Journal of Qualitative Theory of Differential Equations, 2022, no. 47, pp. 1-22, doi.org/10.14232/ejqtde.2022.1.47

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About this paper

Journal

Electronic Journal of Qualitative Theory of Differential Equations

Publisher Name

University of Szeged

Print ISSN

ISSN 14173875

Online ISSN

google scholar link

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