On the existence of periodic solutions under the light of semi-Fredholm operators for some evolution equations

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Mohammed Kriche
Abdelhai El Azzouzi
Khalil Ezzinbi

Abstract

In this work, we investigate the existence of periodic solutions for a class of evolution equations defined as w(t) = (L + C(t))w(t) + H(t). Sufficient conditions on the family of operators {C(t), t ≥ 0}, L and H are proposed to derive the periodicity of solutions from bounded ones on the positive real half-line. The results are obtained by applying the theory of perturbation of semi-Fredholm operators. We suppose that L is a generally nondensely defined operator and satifies the Hille-Yosida condition. Finally, an example of the theoretical findings is presented with numerical simulations.

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How to Cite
Kriche, M., El Azzouzi, A., & Ezzinbi, K. (2025). On the existence of periodic solutions under the light of semi-Fredholm operators for some evolution equations. Gulf Journal of Mathematics, 19(1), 190-207. https://doi.org/10.56947/gjom.v19i1.2531
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