Abstract: In this paper we study a periodic boundary value problem of first order nonlinear differential equations with maxima and discuss the existence and approximation of the solutions. The main result relies on the Dhage iteration method embodied in a recent hybrid fixed point theorem of Dhage (2014) in a partially ordered normed linear space. At the end, we give an example to illustrate th...

In this paper, author proves the algorithms for the existence as well as the approximation of solutions to a couple of periodic boundary value problems of nonlinear first order ordinary integro-differential equations using operator theoretic techniques in a partially ordered metric space. The main results rely on the Dhage iteration method embodied in the recent hybrid fixed point theorems of D...

Abstract: In this paper, the authors prove the existence as well as approximations of the positive solutions for an initial value problem of first-order ordinary nonlinear quadratic differential equations. An algorithm for the solutions is developed and it is shown that the sequence of successive approximations converges monotonically to the positive solution of related quadratic differential e...

In this paper the authors prove existence, uniqueness and approximation of the solutions for initial value problems of nonlinear fractional differential equations with nonlocal conditions, using the operator theoretic technique in a partially ordered metric space. The main results rely on the Dhage iteration principle embodied in the recent hybrid fixed point theorem of Dhage (2014) in a partia...

In this paper we prove the existence and approximation of solution for a nonlinear two point boundary value problem ordinary second order hybrid differential equations with Dirichlet conditions via construction an algorithm solution. The nonlinearity present on right hand side equation is assumed to be Caratho\`eodory proof based monotone iteration method Dhage (2014) in ordered Banach space.

In this work an existence theorem for nth-order ordinary differential inclusions is proved without the continuity of multi-valued functions. Our results are an improvement upon the existence results of Dhage et al. [B.C. Dhage, T.L. Holambe, S.K. Ntouyas, Upper and lower solutions for second order discontinuous differential inclusions, Math. Sci. Res. J. 7 (5) (2003) 206–212] and Agarwal et al....

Using the techniques of some new measures of noncompactness we prove in this paper some existence theorems concerning the global attractivity and ultimate positivity of the solutions for a nonlinear functional integral equation. Our investigations are placed in the Banach space of real-valued functions defined, continuous and bounded on unbounded intervals together with the applications of a re...