Application of‎ ‎multidimensional Hardy operator and its connection with a certain nonlinear differential‎ ‎equation in weighted variable Lebesgue spaces

Abstract

‎In this paper a two weight criterion for multidimensional geometric mean operator in variable exponent‎ ‎Lebesgue space is proved‎. ‎Also‎, ‎we found a criterion on weight functions expressing one-dimensional Hardy‎ ‎inequality via a certain nonlinear differential equation‎. ‎In particular‎, ‎considered nonlinear differential‎ ‎equation is nonlinear integro-differential equation‎.