On a p(x)-Kirchhoff-type Equation with Singular and Superlinear Nonlinearities

In the present paper, we study a p(x)-Kirchhoff-type equation with combined effects of variable singular and superlinear nonlinearities. Using the Ekeland’s variational principle and a constrained minimization approach, we show the existence and uniqueness of a positive solution for the case variable singularity \(\beta (x)\) $\beta (x)$ assumes its values in the interval \((1,\infty )\) $(1,\infty )$ , i.e., the case where \(\beta (x)\) $\beta (x)$ causes a strong singularity.