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

DOI

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/).

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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  -