Existence Results for A Nonlocal Problem Involving the p(x)-Laplacian

Mustafa Avci

doi:doi:10.11648/j.pamj.20130201.13

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Existence Results for A Nonlocal Problem Involving the p(x)-Laplacian

Mustafa Avci

Published in Pure and Applied Mathematics Journal (Volume 2, Issue 1)

Received: 14 January 2013 Accepted: Published: 20 February 2013

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Abstract

In the present paper, we deal with two different existence results of solutions for a nonlocal elliptic Dirichlet boundary value problem involving p(x)-Laplacian. The first one is based on the Brouwer fixed point theorem and the Galerkin method which gives a priori estimate of a nontrivial weak soltion. The second one is based on the variational methods. By using Mountain-Pass theorem, we obtain at least one nontrivial weak soltion.

Published in	Pure and Applied Mathematics Journal (Volume 2, Issue 1)
DOI	10.11648/j.pamj.20130201.13
Page(s)	20-27
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

p(x)-Laplacian; Nonlocal Problem; Fixed Point Theorem; Galerkin Method; Variational Methods Moun-tain-Pass Theorem

References

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Mustafa Avci. (2013). Existence Results for A Nonlocal Problem Involving the p(x)-Laplacian. Pure and Applied Mathematics Journal, 2(1), 20-27. https://doi.org/10.11648/j.pamj.20130201.13

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ACS Style

Mustafa Avci. Existence Results for A Nonlocal Problem Involving the p(x)-Laplacian. Pure Appl. Math. J. 2013, 2(1), 20-27. doi: 10.11648/j.pamj.20130201.13

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AMA Style

Mustafa Avci. Existence Results for A Nonlocal Problem Involving the p(x)-Laplacian. Pure Appl Math J. 2013;2(1):20-27. doi: 10.11648/j.pamj.20130201.13

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@article{10.11648/j.pamj.20130201.13,
  author = {Mustafa Avci},
  title = {Existence Results for A Nonlocal Problem Involving the p(x)-Laplacian},
  journal = {Pure and Applied Mathematics Journal},
  volume = {2},
  number = {1},
  pages = {20-27},
  doi = {10.11648/j.pamj.20130201.13},
  url = {https://doi.org/10.11648/j.pamj.20130201.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20130201.13},
  abstract = {In the present paper, we deal with two different existence results of solutions for a nonlocal elliptic Dirichlet boundary value problem involving p(x)-Laplacian. The first one is based on the Brouwer fixed point theorem and the Galerkin method which gives a priori estimate of a nontrivial weak soltion. The second one is based on the variational methods. By using Mountain-Pass theorem, we obtain at least one nontrivial weak soltion.},
 year = {2013}
}

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TY  - JOUR
T1  - Existence Results for A Nonlocal Problem Involving the p(x)-Laplacian
AU  - Mustafa Avci
Y1  - 2013/02/20
PY  - 2013
N1  - https://doi.org/10.11648/j.pamj.20130201.13
DO  - 10.11648/j.pamj.20130201.13
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 20
EP  - 27
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20130201.13
AB  - In the present paper, we deal with two different existence results of solutions for a nonlocal elliptic Dirichlet boundary value problem involving p(x)-Laplacian. The first one is based on the Brouwer fixed point theorem and the Galerkin method which gives a priori estimate of a nontrivial weak soltion. The second one is based on the variational methods. By using Mountain-Pass theorem, we obtain at least one nontrivial weak soltion.
VL  - 2
IS  - 1
ER  -

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Author Information

Mustafa Avci

Department of Mathematics, Dicle University, Diyarbakir, Turkey

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Plain Text BibTeX RIS

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Mustafa Avci. (2013). Existence Results for A Nonlocal Problem Involving the p(x)-Laplacian. Pure and Applied Mathematics Journal, 2(1), 20-27. https://doi.org/10.11648/j.pamj.20130201.13

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ACS Style

Mustafa Avci. Existence Results for A Nonlocal Problem Involving the p(x)-Laplacian. Pure Appl. Math. J. 2013, 2(1), 20-27. doi: 10.11648/j.pamj.20130201.13

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AMA Style

Mustafa Avci. Existence Results for A Nonlocal Problem Involving the p(x)-Laplacian. Pure Appl Math J. 2013;2(1):20-27. doi: 10.11648/j.pamj.20130201.13

Copy | Download

@article{10.11648/j.pamj.20130201.13,
  author = {Mustafa Avci},
  title = {Existence Results for A Nonlocal Problem Involving the p(x)-Laplacian},
  journal = {Pure and Applied Mathematics Journal},
  volume = {2},
  number = {1},
  pages = {20-27},
  doi = {10.11648/j.pamj.20130201.13},
  url = {https://doi.org/10.11648/j.pamj.20130201.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20130201.13},
  abstract = {In the present paper, we deal with two different existence results of solutions for a nonlocal elliptic Dirichlet boundary value problem involving p(x)-Laplacian. The first one is based on the Brouwer fixed point theorem and the Galerkin method which gives a priori estimate of a nontrivial weak soltion. The second one is based on the variational methods. By using Mountain-Pass theorem, we obtain at least one nontrivial weak soltion.},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - Existence Results for A Nonlocal Problem Involving the p(x)-Laplacian
AU  - Mustafa Avci
Y1  - 2013/02/20
PY  - 2013
N1  - https://doi.org/10.11648/j.pamj.20130201.13
DO  - 10.11648/j.pamj.20130201.13
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 20
EP  - 27
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20130201.13
AB  - In the present paper, we deal with two different existence results of solutions for a nonlocal elliptic Dirichlet boundary value problem involving p(x)-Laplacian. The first one is based on the Brouwer fixed point theorem and the Galerkin method which gives a priori estimate of a nontrivial weak soltion. The second one is based on the variational methods. By using Mountain-Pass theorem, we obtain at least one nontrivial weak soltion.
VL  - 2
IS  - 1
ER  -

Copy | Download