Singular p(x)-Laplacian equation with application to boundary layer theory

In thispaper, we study a singular (Formula presented.) -Laplacian equation that incorporates both variable singular and superlinear nonlinearities. By applying Ekeland’s variational principle and a constrained minimization approach, we establish the existence and uniqueness of a positive solution when the variable singularity (Formula presented.) is within the interval (Formula presented.). As an application of our results, we provide two examples from the basic problem in the boundary layer theory of these pseudoplastic fluids with the no-slip boundary condition at both plates.