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Existence and Differentiability of Solutions for Nondensely Defined Neutral Integro-Differential Evolution Equations

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Abstract

This paper is concerned with the existence, continuous dependence and differentiability of solutions for a semilinear neutral integro-differential evolution equation with nonlocal conditions. It is assumed that the linear part of the considered equation is not densely defined but satisfies the resolvent estimates of the Hille–Yosida condition. The results are established by applying the theory of integrated resolvent operators and Banach fixed point theorem. An example is provided in the end to illustrate the applications of the obtained results.

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Authors and Affiliations

  1. College of Mathematics Science, Inner Mongolia Normal University, Hohhot, 010022, People’s Republic of China

    Jianbo Zhu

  2. School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, 200241, People’s Republic of China

    Xianlong Fu

Authors
  1. Jianbo Zhu
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  2. Xianlong Fu
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Correspondence to Xianlong Fu.

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Communicated by Rosihan M. Ali.

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This work is supported by Science and Technology Commission of Shanghai Municipality (STCSM) (Grant No. 22DZ2229014).

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Zhu, J., Fu, X. Existence and Differentiability of Solutions for Nondensely Defined Neutral Integro-Differential Evolution Equations. Bull. Malays. Math. Sci. Soc. 46, 30 (2023). https://doi.org/10.1007/s40840-022-01428-4

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  • DOI: https://doi.org/10.1007/s40840-022-01428-4

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