Infinitely many solutions for nonlinear fractional boundary value problems via variational methods

被引：6
|
作者：
Chai, Guoqing [1 ]
机构：
[1] Hubei Normal Univ, Coll Math & Stat, Huangshi 435002, Hubei, Peoples R China
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2016年
关键词：
fractional differential equations; variant fountain theorems; critical point theory; variational method; DISPERSION; EXISTENCE;
D O I：
10.1186/s13662-016-0917-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, the author considers the following nonlinear fractional boundary value problem: {d/dt (1/20D(t)(-beta) (u'(t)) + 1/2tD(T)(-beta) (u'(t))) + del F(t, u(t)) = 0, a.e.t is an element of [0, T], u(0) = u(T) = 0, where D-0(t)-beta and D-t(T)-beta are the left and right Riemann-Liouville fractional integrals of order 0 <= beta < 1, respectively, del F(t, x) is the gradient of F at x. By applying the variant fountain theorems, the author obtains the existence of infinitely many small or high energy solutions to the above boundary value problem.
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页数：23
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