Existence theorems for nth-order discontinuous ordinary differential inclusions

AbstractIn 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. [R.P. Agarwal, B.C. Dhage, D. O’Regan, The method of upper and lower solution for differential inclusions via a lattice fixed point theorem, Dynam. Systems Appl. 12 (2003) 1–7] under weaker conditions

Dhage Iteration Method for Nonlinear First Order Hybrid Differential Equations with a Linear Perturbation of Second Type

In this paper the authors prove algorithms for the existence and approximation of the solutions for an initial and a periodic boundary value problem of nonlinear first order ordinary hybrid differential equations with a linear perturbation of second type via Dhage iteration method. Examples are furnished to illustrate the hypotheses and main abstract results of this paper

On N-th order nonlinear ordinary random differential equations

In this paper, an existence result for a nonlinear n-th order ordinary random differential equation is proved under Caratheodory condition. Two existence results for extremal random solutions are also proved for ´ Caratheodory as well as discontinuous cases of the nonlinearity involved in the equations. Our investigations are placed in the Banach space of continuous real-valued functions on closed and bounded intervals of real line together with the application of random version of Leray – Schauder principle.Доведено результат про iснування розв’язку нелiнiйного звичайного випадкового диференцiального рiвняння за виконання умови Каратеодорi. Наведено два результати про iснування екстремальних випадкових розв’язкiв: у випадку виконання умови Каратеодорi та у випадку, коли нелiнiйнiсть не є неперервною. Дослiдження проведено в банаховому просторi неперервних дiйснозначних функцiй на замкнених i обмежених iнтервалах дiйсної осi з застосуванням випадкової версiї принципу Лере – Шаудера

Existence and attractivity results for nonlinear first order random differential equations

In this paper, the existence and attractivity results are proved for nonlinear first order ordinary random differential equations. An example is indicated to demonstrate a realization of the abstract theory developed in the present paper.Викладено результати про iснування та атракторнiсть розв’язкiв нелiнiйних стохастичних диференцiальних рiвнянь першого порядку. Наведено приклад реалiзацiї абстрактної теорiї

On Monch type multi-valued maps and fixed points

AbstractIn this work, some fixed point theorems for a new class of Chandrabhan maps are proved which in turn include the fixed point theorems of Monch, Sadovskii, Darbo, Krasnoselskii, Dhage, and Covitz and Nadler as special cases

Hybrid fixed point theory for strictly monotone increasing multi-valued mappings with applications

AbstractIn this paper, a general hybrid fixed point theorem for the strict monotone increasing multi-valued mappings in ordered Banach spaces is proved via measure of noncompactness and it is further applied to perturbed functional nonconvex differential inclusions for proving the existence results for the extremal solutions under mixed Lipschitz, compactness and strict monotonic conditions

Dhage Iteration Method for Nonlinear First Order Hybrid Differential Equations with a Linear Perturbation of Second Type

In this paper the authors prove algorithms for the existence and approximation of the solutions for an initial and a periodic boundary value problem of nonlinear first order ordinary hybrid differential equations with a linear perturbation of second type via Dhage iteration method. Examples are furnished to illustrate the hypotheses and main abstract results of this paper

Fixed-point theorems for discontinuous multivalued operators on ordered spaces with applications

AbstractIn this paper, some fixed-point theorems for discontinuous multivalued operators on ordered spaces are proved. These theorems improve the earlier known fixed-point theorems of [1,2]. The main fixed-point theorems are applied to first-order discontinuous differential inclusions for proving the existence of extremal solutions under certain monotonicity conditions