Bounded and Zero-Convergent Solutions of a Class of Stieltjes Integro-Differential Equations

Abstract

Abstract. We consider asymptotic properties of solutions to a class of nonlinear Stieltjes integro-differential equations. Necessary and sufficient conditions are given which guarantee that there exist solutions which do (or do not) have nonzero limits at oo . These extend earlier results of various authors and apply to linear and nonlinear difference equations as well.

Some properties of Urysohn‐Stieltjes integral operators

“…The investigations of this paper form a continuation of the study from the paper of Bana and Dronka [15], where we have considered the integral operators of Fredholm-Stieltjes and Hammerstein-Stieltjes type Moreover, we correct some errors made in the above quoted paper so j. SAAG The results of the present paper generalize several ones obtained previously in the papers of Bana and Dronka [15], Bielecki [10]; Chen et al [7]; D]otko [11,12]; Krasnosel'skii et al [2], Ladde et al. [3], Mingarelli [9]; Mykis [14] and Zabrejko et al [5], among others.…”

“…On the other hand in the literature one can meet several papers or books devoted to the study of integral operators of Stieltjes type with kernels of integrals involved depending mostly on one variable (see, for example, Sitzer [6]; Chen et al [7]; Macnerney [8} and Mingarelli [9]).…”