Mechanical Interpretation of Existence Theorems in a Nonlinear Dirichlet Problem

Abstract

The existence of radial solutions to a nonlinear Dirichlet problem in a ball is translated to the language of Mechanics, i.e. to requirements on the time of motion of a particle in an external potential and under the action of a viscosity force. This approach provides a qualitative, but rigorous, method for the analysis of the general case. Known theorems are easily reproduced and examples of new theorems are given, which prove the usefulness of this qualitative method.