Abstract
In this paper, we investigate the existence and Ulam–Hyers–Rassias stability results for a class of functional integrodifferential evolution equations with state-dependent delay and non-instantaneous impulsions on infinite intervals via resolvent operators in the sense of Grimmer. Our analysis is based on fixed point theorem with measures of noncompactness and Picard operators. Moreover, an illustrative example is considered to support our new results.
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Bensalem, A., Salim, A. & Benchohra, M. Ulam–Hyers–Rassias Stability of Neutral Functional Integrodifferential Evolution Equations with Non-instantaneous Impulses on an Unbounded Interval. Qual. Theory Dyn. Syst. 22, 88 (2023). https://doi.org/10.1007/s12346-023-00787-y
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DOI: https://doi.org/10.1007/s12346-023-00787-y
Keywords
- Ulam–Hyers–Rassias stability
- Fixed point theorem
- Infinite delay
- Integrodifferential equation
- Measures of noncompactness
- Mild solution
- Resolvent operator
- State-dependent delay