Quasi-solutions for generalized second order differential equations with deviating arguments

Abstract

This paper deal with boundary value problems for generalized second order differential equations with deviating arguments. Existence of quasi-solutions and solutions are proved by monotone iterative method. Examples with numerical results are added.

Nonlinear perturbed integral equations related to nonlocal boundary value problems

“…On the other hand, BVPs where nonlocal terms occur in the differential equation have been studied by a number of authors. For example, the case of equations with reflection of the argument has been investigated by Andrade and Ma [3], Cabada and co-authors [6], Piao [45,46], Piao and Xin [47], Wiener and Aftabizadeh [61], the case of equations with deviated arguments has be en studied by Jankowski [34][35][36], Figueroa and Pouso [14] and Szatanik [51,52] and the case of equations that involve the average of the solution has been considered by Andrade and Ma [3], Chipot and Rodrigues [8] and Infante [27].…”

Nonzero solutions of perturbed Hammerstein integral equations with deviated arguments and applications

“…The existence of solutions of boundary value problems (BVPs) with deviated arguments has been investigated recently by a number of authors using the upper and lower solutions method [15], monotone iterative methods [34,39,59, 60] 1 , the classic Avery-Peterson Theorem [35,36,37,38] or, in the special case of reflections, the classical fixed point index [9].…”