DOI: 10.1002/mma.70911 ISSN: 0170-4214
On Abstract Integro‐Differential Equations With State‐Dependent Integral Terms
Shashank Pandey, D. N. PandeyABSTRACT
We develop a framework for abstract integro‐differential equations with state‐dependent integration intervals and demonstrate its applicability to partial differential equations. Using Banach's contraction principle and the Schauder fixed‐point theorem, we prove local existence and uniqueness and establish local well‐posedness for both mild and strict solutions. The paper concludes with examples drawn from population dynamics that illustrate the theory.