On the localization and numerical computation of positive radial solutions for $\phi $-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 $\phi $-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'skii's 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.

Keywords

• $\phi $-laplace operator
• radial solution
• positive solution
• fixed point index
• harnack type inequality
• numerical solution