The Multiplicity of Solutions for a Certain Class of Fractional Elliptic Equation
Shifeng Zhang, Zhiyang Jia, Jihe Wang
Available Online May 2016.
- 10.2991/amsm-16.2016.18How to use a DOI?
- fractional laplace's equation; dirichlet boundary value condition; mountain pass theorem; positive solution; negative solution
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.
- © 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 - 10.2991/amsm-16.2016.18 ID - Zhang2016/05 ER -