Existence and classifiction of radial solutions of a nonlinear nonautonomous Dirichlet problem

TL;DR

This paper extends the classification of radial solutions for superlinear Dirichlet problems to nonautonomous cases, using a priori estimates to establish existence and classification results that generalize previous autonomous cases.

Contribution

It introduces a new approach based on a priori estimates to classify solutions of nonautonomous superlinear Dirichlet problems, broadening the scope of previous autonomous results.

Findings

Classification of solutions extends to nonautonomous problems.

Existence and uniqueness results are preserved under new conditions.

A priori estimates are key to the classification method.

Abstract

This paper generalizes a classification of solutions of a superlinear Dirichlet problem given in \cite{rouaki2} to a nonautonomous case. In \cite{rouaki1} the increasing of $f(t)$ was used to prove the classification and in \cite{rouaki2} the unicity of the solution of the \emph{Cauchy} problem was used. Here the classification appears as a consequence of the \emph{a priori} estimates. It results that existence classificarion remain true for a class of nonautonomous problems.