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Existence of Solutions for an Impulsive p-laplacian Equation with Nonresonance Conditions

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Abstract

This paper deals with a nonresonance problem given in the shape of a nonlinear impulsive differential equation with Dirichlet boundary conditions. After giving a characterization of the first eigenvalue \(\lambda _1\) for an intermediary eigenvalue problem with some properties related to \(\lambda _1\) such as simplicity, isolation, strict monotonicity and that the first eigenfunction \(u_1\) which correspond to \(\lambda _1\) has a constant sign, also by the characterization of the second eigenvalue \(\lambda _2\) and its strictly partial monotonicity, we prove existence of at least one solution to our problem by using variational approach. Finally, we give a few examples to illustrate our main theorems.

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Acknowledgements

The authors thank the reviewers for attentively reading the paper, and for giving pertinent remarks and precious ideas to enhance the results as well as the presentation of this work.

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  1. Omar Chakrone and Mohammed Chehabi have contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, LaMAO, Faculty of Science, University Mohammed First, Oujda, Morocco

    Mohamed Bouabdallah, Omar Chakrone & Mohammed Chehabi

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  1. Mohamed Bouabdallah
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  2. Omar Chakrone
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  3. Mohammed Chehabi
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The authors declare that the research was carried out in cooperation with the same accountability. All authors have seen and approved the final paper.

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Correspondence to Mohamed Bouabdallah.

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Bouabdallah, M., Chakrone, O. & Chehabi, M. Existence of Solutions for an Impulsive p-laplacian Equation with Nonresonance Conditions. Differ Equ Dyn Syst (2023). https://doi.org/10.1007/s12591-023-00660-z

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