The existence of a ground state solution for a class of fractional differential equation with p -Laplacian operator

Boundary value problems

Zhigang Hu¹  Wenbin Liu¹  Taiyong Chen¹ 

[1] Department of Mathematics, China University of Mining and Technology, Xuzhou, P.R. China

关键词: fractional differential equations;    boundary value problem;    Nehari manifold;    ground state solution;    34A08;    35A15;   

DOI  :  10.1186/s13661-016-0557-z

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we apply the Nehari manifold method to study the fractional p-Laplacian differential equation{DTαtϕp(0Dtαu(t))=f(t,u(t)),t∈[0,T],u(0)=u(T)=0,$$ \left \{ \textstyle\begin{array}{ll} {}_{t}D_{T}^{\alpha}\phi_{p}({}_{0}D_{t}^{\alpha}u(t))=f(t,u(t)), \quad t\in[0,T], \\ u(0)=u(T)=0, \end{array}\displaystyle \right . $$whereDtα0${}_{0}D_{t}^{\alpha}$,DTαt${}_{t}D_{T}^{\alpha}$are the left and right Riemann-Liouville fractional derivatives of order0≤α<1$0\leq\alpha<1$, respectively. We prove the existence of a ground state solution for the boundary value problem.

【 授权许可】

CC BY