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
Consider the system with three-component integral equations{u（x） ：fRn│x - y│α-nw（y）^v（y）^qdy,v（x） =fRn│x-y│^α-nu（y）^pw（y）^rdy, w（x） =fRn│x - y│α-nv（y）qu（y）Pdy,where 0 〈 a 〈 n, n is a posi...Consider the system with three-component integral equations{u（x） ：fRn│x - y│α-nw（y）^v（y）^qdy,v（x） =fRn│x-y│^α-nu（y）^pw（y）^rdy, w（x） =fRn│x - y│α-nv（y）qu（y）Pdy,where 0 〈 a 〈 n, n is a positive constant, p, q and r satisfy some suitable conditions. It is shown that every positive regular solution （u（x）, v（x）, w（x）） is radially symmetric and monotonic about some point by developing the moving plane method in an integral form. In addition, the regularity of the solutions is also proved by the contraction mapping principle. The conformal invariant property of the system is also investigated.展开更多
Consider the system of integral equations with weighted functions in Rn,{u(x) =∫Rn|x-y|α-nQ(y)v(y)qdy1,v(x)=∫Rn|x-y|α-nK(y)u(y)pdy,where 0 < α < n,1/(p+1) + 1/(q+1)≥(n-α)/n1,α/(n-α) < p1q < ∞1,Q(...Consider the system of integral equations with weighted functions in Rn,{u(x) =∫Rn|x-y|α-nQ(y)v(y)qdy1,v(x)=∫Rn|x-y|α-nK(y)u(y)pdy,where 0 < α < n,1/(p+1) + 1/(q+1)≥(n-α)/n1,α/(n-α) < p1q < ∞1,Q(x) and K(x) satisfy some suitable conditions.It is shown that every positive regular solution(u(x)1,v(x)) is symmetric about some plane by developing the moving plane method in an integral form.Moreover,regularity of the solution is studied.Finally,the nonexistence of positive solutions to the system in the case 0 < p1q <(n+α)/(n-α) is also discussed.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 National National Science Foundation of China for Distinguished Young Scholars (Grant No. 10925104)National National Science Foundation of China (Grant No.11101319)the Foundation of Shaanxi Province Education Department (Grant No. 2010JK549)
文摘Consider the system with three-component integral equations{u（x） ：fRn│x - y│α-nw（y）^v（y）^qdy,v（x） =fRn│x-y│^α-nu（y）^pw（y）^rdy, w（x） =fRn│x - y│α-nv（y）qu（y）Pdy,where 0 〈 a 〈 n, n is a positive constant, p, q and r satisfy some suitable conditions. It is shown that every positive regular solution （u（x）, v（x）, w（x）） is radially symmetric and monotonic about some point by developing the moving plane method in an integral form. In addition, the regularity of the solutions is also proved by the contraction mapping principle. The conformal invariant property of the system is also investigated.
基金supported by Chinese National Science Fund for Distinguished Young Scholars (Grant No.10925104)National Natural Science Foundation of China (Grant No.11001221)+1 种基金the Foundation of Shaanxi Province Education Department (Grant No. 2010JK549)the Foundation of Xi’an Statistical Research Institute (Grant No.10JD04)
文摘Consider the system of integral equations with weighted functions in Rn,{u(x) =∫Rn|x-y|α-nQ(y)v(y)qdy1,v(x)=∫Rn|x-y|α-nK(y)u(y)pdy,where 0 < α < n,1/(p+1) + 1/(q+1)≥(n-α)/n1,α/(n-α) < p1q < ∞1,Q(x) and K(x) satisfy some suitable conditions.It is shown that every positive regular solution(u(x)1,v(x)) is symmetric about some plane by developing the moving plane method in an integral form.Moreover,regularity of the solution is studied.Finally,the nonexistence of positive solutions to the system in the case 0 < p1q <(n+α)/(n-α) is also discussed.
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.
