Connection of two nonlinear differential equations with a two-dimensional Hardy operator in weighted Lebesgue spaces with mixed norms

Abstract

In this article we study a connection between two nonlinear differential equations with a two-dimensional Hardy operator in weighted Lebesgue spaces with mixed norm. In particular, it is proved that the weight functions which are the coefficients of nonlinear differential equations are included in the estimate of the two-dimensional Hardy operator in this space.

Keywords

• Two-dimensional Hardy operator
• weight functions
• Lebesgue spaces with mixed norm