On existence results and qualitative properties of mild solution of semilinear mixed Volterra-Fredholm functional integrodifferential equations in Banach spaces. (English) Zbl 1298.45017
Summary: We prove the existence results, uniqueness, continuous dependence on initial functions and on parameters of mild solution of semilinear mixed Volterra-Fredholm functional integrodifferential equations in Banach spaces. The closeness and continuous dependence of the mild solution on the right-hand side of the equation is also established. Our analysis is based on the theory of strongly continuous semigroup, the nonlinear alternative of Leray-Schauder and the integral inequality established by Pachpatte. An example is given to illustrate the results.
MSC:
| 45N05 | Abstract integral equations, integral equations in abstract spaces |
| 45J05 | Integro-ordinary differential equations |
| 45B05 | Fredholm integral equations |
| 45D05 | Volterra integral equations |
Keywords:
Volterra-Fredholm equations; strongly continuous semigroup; nonlinear alternative; continuous dependence; closeness; Pachpatte’s inequalityReferences:
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