Application of multidimensional Hardy operator and its connection with a   certain nonlinear differential equation in weighted variable Lebesgue spaces
  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. 
Bandaliyev Rovshan
math.CA