Difference equations and nonexistence of solutions of an integral equation

Abstract

By using difference equations, we give some easily applicable sufficient conditions for the non-existence of nonnegative solutions satisfying some additional conditions, of the integral equationf(x)=∫ X(a(x,t) +b(x,t)|f(t)| p)dμ(t),where p≥1 and X is a measurable space with probability measure μ.