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Nonlocal eigenvalue type problem in fractional Orlicz-Sobolev space

Nonlocal eigenvalue type problem

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Abstract

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

$$\begin{aligned} (P_a) \left\{ \begin{array}{clclc} (-\varDelta )^s_a u +a(|u|)u = \lambda f(x,u) &{} \text { in }&{} \varOmega , \\ u = 0 &{} \text { in } &{} {\mathbb {R}} ^N\setminus \varOmega . \end{array} \right. \end{aligned}$$

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

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Authors and Affiliations

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

    Elhoussine Azroul, Abdelmoujib Benkirane & Mohammed Srati

Authors
  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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Communicated by Julio Rossi.

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Azroul, E., Benkirane, A. & Srati, M. Nonlocal eigenvalue type problem in fractional Orlicz-Sobolev space. Adv. Oper. Theory 5, 1599–1617 (2020). https://doi.org/10.1007/s43036-020-00067-5

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  • DOI: https://doi.org/10.1007/s43036-020-00067-5

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