NONLINEAR ABSTRACT MEASURE HYBRID DIFFERENTIAL EQUATIONS WITH A LINEAR PERTURBATION OF SECOND TYPE
Bapurao C. Dhage
‘Kasubai’, Gurukul Colony, Thodga Road,
Ahmedpur - 413515, Distr. Latur
(Received : July 22, 2020 ; Revised: September 17, 2020)
In this paper, an existence result for perturbed abstract measure differential equations is proved via hybrid fixed point theorems of Dhage  under the mixed generalized Lipschitz and Carathéodory conditions. The existence of the extremal solutions is also proved under certain monotonicity conditions and using a hybrid fixed point theorem of Dhage  on ordered Banach spaces. Our existence results include the existence results of Sharma , Joshi  and Shendge and Joshi  as special cases under weaker continuity condition.
2010 Mathematics Subject Classifications: 34K10, 47H10
Keywords and phrases: Abstract measure differential equation; Dhage fixed point theorem; Existence theorem; Extremal solutions.
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