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

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In thispaper, we study a singular p ( x ) -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 β ( x ) is within the interval ( 1 , ∞ ) . 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.