On a $p(x)$-Kirchhoff Problem with Variable Singular and Sublinear Exponents

Abstract

In the present paper, we study a singular $p(x)$-Kirchhoff equation with combined effects of variable singular, $\beta(x)$, and sublinear, $q(x)$, nonlinearities. Using the Ekeland's variational principle and a constrained minimization, we show the existence of a positive solution for the case variable singularity $\beta(x)$ assumes its values in the interval $(1,\infty)$. We provide an example to illustrate our results.