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Existence Results for Some Partial Integro-Differential Equations

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Abstract

In this note, we deal with semilinear integro-differential equations subject to homogeneous Dirichlet boundary conditions given on the boundaries of the sections. Even if the differentiation will be taken only in some directions, it is not possible to see the main problem parameterized by the other coordinates because of the non-local terms which also obliged the problem to be degenerate. We establish the existence of solutions by employing the singular perturbations method as a natural tool. The perturbed problems are classical, non-local, semilinear elliptic problems and the limits of the subsequences of their solutions, in weighted Sobolev type spaces, are solutions of the main problem. Some improvement, concerning the existence of the solutions and the convergence results depending on the weights, will be established. The paper also gives an idea about the study of the anisotropic singular perturbations in the framework of weighted spaces.

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Authors and Affiliations

  1. Mathematics Department, College of Sciences, Qassim University, Al-Qassim, Saudi Arabia

    Senoussi Guesmia

  2. Laboratoire AMNEDP, Faculté de Mathématiques, USTHB, B.P. 32, El Alia, Bab Ezzouar, 16123, Algiers, Algeria

    Rokia Kechkar & Mohamed Said Moulay

Authors
  1. Senoussi Guesmia
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  2. Rokia Kechkar
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  3. Mohamed Said Moulay
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Correspondence to Senoussi Guesmia.

Additional information

S. Guesmia has been supported by the university of Qassim under the contract SR-D-2219/1434.

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Guesmia, S., Kechkar, R. & Moulay, M.S. Existence Results for Some Partial Integro-Differential Equations. Mediterr. J. Math. 13, 4063–4079 (2016). https://doi.org/10.1007/s00009-016-0732-6

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  • DOI: https://doi.org/10.1007/s00009-016-0732-6

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