Abstract
This paper deals with some existence of mild solutions for two classes of impulsive integrodifferential equations in Banach spaces. Our results are based on the fixed point theory and the concept of measure of noncompactness with the help of the resolvent operator. Two illustrative examples are given in the last section.
Highlights
The existence of mild solutions is developed in [1, 2] for some semilinear functional differential equations
There has been a significant development in functional evolution equations in recent years
Due to nonlocal problems having a wide range of applications in real-world applications, evolution equations with nonlocal initial conditions were studied by many authors
Summary
The existence of mild solutions is developed in [1, 2] for some semilinear functional differential equations. As a matter of fact, it is demonstrated that the evolution equations with nonlocal initial conditions have better effects in applications than the classical Cauchy problems. Xue [16] studied the existence of mild solutions for semilinear differential equations with nonlocal initial conditions in separable Banach spaces. We first discuss the existence of mild solutions for the following nonlocal problem of impulsive integrodifferential equations. Abstract and Applied Analysis norm ∥·∥, u′ðtÞ ≔ du/dt, A : DðAÞ ⊂ E ⟶ E generates a C0 -semigroup on the Banach space E, and YðtÞ is a closed linear operator on E with DðAÞ ⊂ DðYÞ: In [26,27,28,29] the authors initially offered to study some classes of impulsive differential equations with noninstantaneous impulses. Motivated by the above papers, we discuss the existence of mild solutions for the following nonlocal problem of noninstantaneous impulsive integrodifferential equations:.
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