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Ekeland’s variational principle for a nonlocal p-Kirchhoff type eigenvalue problem

Ekeland’s variational principle

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Abstract

This paper is concerned with a class of fractional p-Laplace type problems with Dirichlet boundary data of the following form

$$\begin{aligned} (P_s) \hspace{0.5cm} \left\{ \begin{array}{clclc} M(||u||^p)\left( (-\Delta )^s_p u +|u|^{p-2}u\right) &{}=&{} \lambda f(x,u) &{} \text { in }&{} \Omega \\ \\ \hspace{1cm} u &{} = &{} 0 \hspace{0.2cm} \hspace{0.2cm} &{} \text { in } &{} {\mathbb {R}}^N\setminus \Omega . \end{array} \right. \end{aligned}$$

By means of Ekeland’s variational principle and a direct variational approach, we investigate the existence of nontrivial weak solution for the above problem.

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Authors and Affiliations

  1. Sidi Mohamed Ben Abdellah University, Faculty of Sciences Dhar El Mahraz, Laboratory of Mathematical Analysis and Applications, Fez, Morocco

    Elhoussine Azroul & Abdelmoujib Benkirane

  2. High School of Education and Formation (ESEF), University Mohammed First, Oujda, Morocco

    Mohammed Srati

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  1. Elhoussine Azroul
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  2. Abdelmoujib Benkirane
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  3. Mohammed Srati
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Correspondence to Mohammed Srati.

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Azroul, E., Benkirane, A. & Srati, M. Ekeland’s variational principle for a nonlocal p-Kirchhoff type eigenvalue problem. Rend. Circ. Mat. Palermo, II. Ser 73, 1241–1254 (2024). https://doi.org/10.1007/s12215-023-00984-3

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