On a generalized Kirchhoff equation with sublinear nonlinearities

TL;DR

This paper studies a generalized Kirchhoff equation with sublinear nonlinearities, showing it can be transformed into a classical semilinear equation for easier analysis under certain conditions.

Contribution

It demonstrates a method to reduce a complex Kirchhoff equation with sublinear terms to a standard semilinear form, facilitating analysis.

Findings

Reduction of the generalized Kirchhoff equation to a classical semilinear equation.

Applicable under specific assumptions on the data.

Simplifies the study of such equations using standard tools.

Abstract

In this paper we consider a generalized Kirchhoff? equation in a bounded domain under the effect of a sublinear nonlinearity. Under suitable assumptions on the data of the problem we show that, with a simple change of variable, the equation can be reduced to a classical semilinear equation and then studied with standard tools.