Proceedings of the 2016 International Conference on Applied Mathematics, Simulation and Modelling

The Multiplicity of Solutions for a Certain Class of Fractional Elliptic Equation

Authors
Shifeng Zhang, Zhiyang Jia, Jihe Wang
Corresponding Author
Shifeng Zhang
Available Online May 2016.
DOI
https://doi.org/10.2991/amsm-16.2016.18How to use a DOI?
Keywords
fractional laplace's equation; dirichlet boundary value condition; mountain pass theorem; positive solution; negative solution
Abstract

This paper explores the multiplicity of solutions for a Certain class of fractional elliptic equation under the Dirichlet boundary conditions. By using the asymptotic property of the nonlinear term f(x,u) at zero and at infinite point, the mountain pass theorem and proper truncation methods can be applied to get both a positive and a negative solution for all parameters under the condition of not satisfying the Ambrosetti-Rabinowitz.

Copyright
© 2016, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Download article (PDF)

Volume Title
Proceedings of the 2016 International Conference on Applied Mathematics, Simulation and Modelling
Series
Advances in Computer Science Research
Publication Date
May 2016
ISBN
978-94-6252-198-8
ISSN
2352-538X
DOI
https://doi.org/10.2991/amsm-16.2016.18How to use a DOI?
Copyright
© 2016, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - CONF
AU  - Shifeng Zhang
AU  - Zhiyang Jia
AU  - Jihe Wang
PY  - 2016/05
DA  - 2016/05
TI  - The Multiplicity of Solutions for a Certain Class of Fractional Elliptic Equation
BT  - Proceedings of the 2016 International Conference on Applied Mathematics, Simulation and Modelling
PB  - Atlantis Press
SP  - 76
EP  - 78
SN  - 2352-538X
UR  - https://doi.org/10.2991/amsm-16.2016.18
DO  - https://doi.org/10.2991/amsm-16.2016.18
ID  - Zhang2016/05
ER  -