In this paper,we consider the following system of integral equations on upper half space {u（x） = ∫Rn ＋ （1/｜x-y｜n-α-1/｜-y｜n-α） λ1up1（y） ＋ μ1vp2（y） ＋ β1up3（y）vp4（y） dy;v（x） = ∫Rn ＋ （1/｜x-y...In this paper,we consider the following system of integral equations on upper half space {u（x） = ∫Rn ＋ （1/｜x-y｜n-α-1/｜-y｜n-α） λ1up1（y） ＋ μ1vp2（y） ＋ β1up3（y）vp4（y） dy;v（x） = ∫Rn ＋ （1/｜x-y｜n-α-1/｜-y｜n-α）（λ2uq1（y） ＋ μ2vq2（y） ＋ β2uq3（y）vq4（y） dy,where Rn ＋ = {x =（x1,x2,...,xn） ∈ Rn｜xn〉 0}, =（x1,x2,...,xn-1,-xn） is the reflection of the point x about the hyperplane xn= 0,0 〈 α 〈 n,λi,μi,βi≥ 0（i = 1,2） are constants,pi≥ 0 and qi≥ 0（i = 1,2,3,4）.We prove the nonexistence of positive solutions to the above system with critical and subcritical exponents via moving sphere method.展开更多
In this paper, we establish the existence result of solution and positive solution for two-point boundary value problem of a semilinear fractional differential equation by using the Leray-Schauder fixed-point theorem....In this paper, we establish the existence result of solution and positive solution for two-point boundary value problem of a semilinear fractional differential equation by using the Leray-Schauder fixed-point theorem. The discussion is based on the system of integral equations on a bounded region.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.11101319,11201081,11202035)the Foundation of Shaanxi Statistical Research Center(Grant No.13JD04)the Foundation of Xi’an University of Finance and Economics(Grant No.12XCK07)
文摘In this paper,we consider the following system of integral equations on upper half space {u（x） = ∫Rn ＋ （1/｜x-y｜n-α-1/｜-y｜n-α） λ1up1（y） ＋ μ1vp2（y） ＋ β1up3（y）vp4（y） dy;v（x） = ∫Rn ＋ （1/｜x-y｜n-α-1/｜-y｜n-α）（λ2uq1（y） ＋ μ2vq2（y） ＋ β2uq3（y）vq4（y） dy,where Rn ＋ = {x =（x1,x2,...,xn） ∈ Rn｜xn〉 0}, =（x1,x2,...,xn-1,-xn） is the reflection of the point x about the hyperplane xn= 0,0 〈 α 〈 n,λi,μi,βi≥ 0（i = 1,2） are constants,pi≥ 0 and qi≥ 0（i = 1,2,3,4）.We prove the nonexistence of positive solutions to the above system with critical and subcritical exponents via moving sphere method.
基金supported by the Natural Science Foundation of China(No.11271235)the Foundation of Datong University(2014Q10)
文摘In this paper, we establish the existence result of solution and positive solution for two-point boundary value problem of a semilinear fractional differential equation by using the Leray-Schauder fixed-point theorem. The discussion is based on the system of integral equations on a bounded region.
