Abstract
Abstract The objective of this article is to discuss the existence and uniqueness of mild solutions for a class of non-autonomous semilinear differential equations with nonlocal condition via monotone iterative method with upper and lower solutions in an ordered complete norm space X, using evolution system and measure of noncompactness.
Highlights
Nonlocal condition is a generalization of classical initial condition which is more effective to produce better results in the application of physical problems rather than classical initial condition
The existence results for nonlocal Cauchy problem was first studied by Byszewski [1]
In [3], authors discussed the existence of mild solutions for a class of fractional evolution equations with nonlocal integral conditions with the help of compact semigroup, approximation technique and Schauder fixed point theorem
Summary
The existence of mild solutions of a non-autonomous integro-differential equations with nonlocal conditions by using the theory of evolution families, Banach contraction principle and Schauder’s fixed point theorem is studied by Yan [14]. In [16], Alka et al established the existence and uniquenss of mild solutions for non-autonomous instantaneous impulsive differential equations with iterated deviating arguments by using analytic semigroup theory and Banach fixed point theorem. Chen et al [19] studied the existence of mild solutions for a class of fractional non-autonomous evolution equations with delay by using analytic semigroup, measure of noncompactness and fixed point theorem with respect to k-set contractive operator. In [21], Chen et al established the existence of mild solutions for a non-autonomous fractional differential equation by using the theory of evolution families and fixed point theorem with respect to k- set contractive operator.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
