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Fractional Evolution Equations with Nonlocal Initial Conditions and Superlinear Growth Nonlinear Terms

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Abstract

We investigate the existence of solutions for a class of fractional evolution equations with nonlocal initial conditions and superlinear growth nonlinear functions in Banach spaces. By using the compactness of semigroup generated by the linear operator, we neither assume any Lipschitz property of the nonlinear term nor the compactness of the nonlocal initial conditions. Moreover, the approximation technique coupled with the Hartmann-type inequality argument allows the treatment of nonlinear terms with superlinear growth. Then combining with the Leray-Schauder continuation principle, we prove the existence results. Finally, the results obtained are applied to fractional parabolic equations with continuous superlinearly growth nonlinearities and nonlocal initial conditions including periodic or antiperiodic conditions, multipoint conditions and integral-type conditions.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (No. 12061063), the Outstanding Youth Science Fund of Gansu Province (No. 21JR7RA159), Funds for Innovative Fundamental Research Group Project of Gansu Province (No. 23JRRA684) and Project of NWNU-LKZD2023-03.

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Authors and Affiliations

  1. Department of Mathematics, Northwest Normal University, Lanzhou, 730070, China

    Pengyu Chen & Wei Feng

  2. Gansu Provincial Research Center for Basic Disciplines of Mathematics and Statistics, Lanzhou, 730070, China

    Pengyu Chen

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  1. Pengyu Chen
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  2. Wei Feng
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P. Chen and W. Feng wrote the main manuscript text. All authors reviewed the manuscript.

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Correspondence to Pengyu Chen.

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Chen, P., Feng, W. Fractional Evolution Equations with Nonlocal Initial Conditions and Superlinear Growth Nonlinear Terms. Qual. Theory Dyn. Syst. 23, 69 (2024). https://doi.org/10.1007/s12346-023-00913-w

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