On an anisotropic $ \overset{\rightarrow }{p}(\cdot) $-Laplace equation with variable singular and sublinear nonlinearities

Abstract

In the present paper, we study an anisotropic $ \overset{\rightarrow }{p}(\cdot) $-Laplace equation with combined effects of variable singular and sublinear nonlinearities. Using the Ekeland's variational principle and a constrained minimization, we show the existence of a positive solution for the case where the variable singularity $ \beta(x) $ assumes its values in the interval $ (1, \infty) $.

Keywords

• anisotropic singular $ \overset{\rightarrow }{p}(\cdot) $-laplacian
• variable strong singularity
• anisotropic variable sobolev space
• ekeland's variational principle