Positive Solutions for a System of Fractional Integral Boundary Value Problems of Riemann-Liouville Type Involving Semipositone Nonlinearities

被引:4
作者
Ding, Youzheng [1 ]
Xu, Jiafa [2 ]
Fu, Zhengqing [3 ]
机构
[1] Shandong Jianzhu Univ, Sch Sci, Jinan 250101, Shandong, Peoples R China
[2] Chongqing Normal Univ, Sch Math Sci, Chongqing 401331, Peoples R China
[3] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Shandong, Peoples R China
基金
中国国家自然科学基金;
关键词
Riemann-Liouville type fractional problem; positive solutions; the index of fixed point; matrix theory; DIFFERENTIAL-EQUATIONS; COUPLED SYSTEM; UNIQUENESS; EXISTENCE;
D O I
10.3390/math7100970
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this work by the index of fixed point and matrix theory, we discuss the positive solutions for the system of Riemann-Liouville type fractional boundary value problems D(0+)(alpha)u(t)+f(1)(t,u(t),v(t),w(t)) = 0,t is an element of(0,1), D(0+)(alpha)v(t)+f(2)(t,u(t),v(t),w(t)) = 0,t is an element of(0,1), D(0+)(alpha)w(t)+f(3)(t,u(t),v(t),w(t)) = 0,t is an element of(0,1), u(0) = u'(0) = center dot center dot center dot = u((n-2))(0) = 0, D(0+)(p)u(t)vertical bar(t=1) = integral(1)(0)h(t)D(0+)(q)u(t)dt, v(0)=v '(0) = center dot center dot center dot = v((n-2))(0) = 0, D(0+)(p)v(t)vertical bar(t=1) = integral(1)(0)h(t)D(0+)(q)v(t)dt, w(0) = w'(0) = center dot center dot center dot = w((n-2))(0)=0, D(0+)(p)w(t)vertical bar(t=1) = integral(1)(0)h(t)D(0+)(q)w(t)dt, where alpha is an element of(n-1,n] with n is an element of N, n >= 3, p,q is an element of R with p is an element of[1, n-2], q is an element of[0, p], D-0+(alpha) is the alpha order Riemann-Liouville type fractional derivative, and f(i)(i=1,2,3) is an element of C([0,1] x R+ x R+x R+, R) are semipositone nonlinearities.
引用
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页数:19
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