Positive solutions of Volterra integral equations using integral inequalities
The authors discuss the existence of positive solutions of certain special cases of the possible singular integral equation \[ y(t)= \int^t_0 k(t, s)[f(y(s))+ g(y(s))] ds,\quad t\in [0,T]. \] They assume that \(f: [0,\infty)\to [0,\infty)\) is continuous and nondecreasing, \(g: [0,\infty)\to [0,\infty)\) is continuous, nonincreasing and possibly singular. For the proof of results in this the authors use the Krasnoselskij's fixed point theorem.
scientific article; zbMATH DE number 1820058