This paper deals with a nonlinear boundary value problem for a complex equation W_z = H(Z,W,W_z),Z ∈G : |Z|<1 with boundary eondition of the form I.l-i Re[Z-W(Z)] = ψ(Z,W(Z)) + Re[λ_0+sum from k=1 to |n|-1(λ_k ...This paper deals with a nonlinear boundary value problem for a complex equation W_z = H(Z,W,W_z),Z ∈G : |Z|<1 with boundary eondition of the form I.l-i Re[Z-W(Z)] = ψ(Z,W(Z)) + Re[λ_0+sum from k=1 to |n|-1(λ_k + iλ_k)Z^k],Z∈Γ:|z|=1 k--1 in which the index is negative. By establishing a priori estimate and using the imbdding method combined with the the Newton interation procedure, it is proved that the above problem is solvable and the solution is unique in C^l+a(g) ,O<a<].展开更多
This paper considers the following boundary value problems for functional differential equations: x' (t) = f(t, xt) (0<t<b) ,x0 = x1, and x'(t) = f(t,xt, x' (t)) (0<t<b) , x0 = , x(b) = B. By u...This paper considers the following boundary value problems for functional differential equations: x' (t) = f(t, xt) (0<t<b) ,x0 = x1, and x'(t) = f(t,xt, x' (t)) (0<t<b) , x0 = , x(b) = B. By using certain fixed point theorem based on degree theory,some sufficient conditions for solvability of the above problems are given.展开更多
In the present paper system and the solutions to the the solvability condition of the linearized Gauss-Codazzi homogenous system are given. In the meantime, the ＇solvability of a relevant linearized Darboux equation...In the present paper system and the solutions to the the solvability condition of the linearized Gauss-Codazzi homogenous system are given. In the meantime, the ＇solvability of a relevant linearized Darboux equation is given. The equations are arising in a geometric problem which is concerned with the realization of the Alexandrov＇s positive annulus in R^3.展开更多
In this paper we examine controllability problems of evolution inclusions with nonlocal conditions. Using Kakutani's fixed point theorem and Schauder's fixed point the-orem, we establish sufficient conditions ...In this paper we examine controllability problems of evolution inclusions with nonlocal conditions. Using Kakutani's fixed point theorem and Schauder's fixed point the-orem, we establish sufficient conditions for the controllability under convex and nonconvex orientor fields respectively.展开更多
This paper presents sensitivity analysis for parameterized variational inequality problems (VIP). Under appropriate assumption, it is shown that the perturbed solution to parameterized VIP is existent, unique, continu...This paper presents sensitivity analysis for parameterized variational inequality problems (VIP). Under appropriate assumption, it is shown that the perturbed solution to parameterized VIP is existent, unique, continuous and differentiable with respect to perturbation parameter. In the case of differentiability, we derive the equations for calculating the derivative of solution variables with respect to the perturbation parameters.展开更多
The author introduces a concept of curvature bound set relative to second order impulsive differential systems and based on this concept discusses the existence of solutions to the Picard boundary value problem of the...The author introduces a concept of curvature bound set relative to second order impulsive differential systems and based on this concept discusses the existence of solutions to the Picard boundary value problem of the systems. Compared with the previous works finished by Lakshmikantham and Erbe, the author's results do not require the right handed function and impulsive functions with special structures such as monotonicity, etc. When the impulsive effects are absent, these results could be viewed as new generalized forms of the two so called optimal results about second order scalar differential equations derived by Lees and Mawhin respectively.展开更多
文摘This paper deals with a nonlinear boundary value problem for a complex equation W_z = H(Z,W,W_z),Z ∈G : |Z|<1 with boundary eondition of the form I.l-i Re[Z-W(Z)] = ψ(Z,W(Z)) + Re[λ_0+sum from k=1 to |n|-1(λ_k + iλ_k)Z^k],Z∈Γ:|z|=1 k--1 in which the index is negative. By establishing a priori estimate and using the imbdding method combined with the the Newton interation procedure, it is proved that the above problem is solvable and the solution is unique in C^l+a(g) ,O<a<].
文摘This paper considers the following boundary value problems for functional differential equations: x' (t) = f(t, xt) (0<t<b) ,x0 = x1, and x'(t) = f(t,xt, x' (t)) (0<t<b) , x0 = , x(b) = B. By using certain fixed point theorem based on degree theory,some sufficient conditions for solvability of the above problems are given.
基金Project supported by the National Natural Science Foundation of China (No. 11101068)the Fundamental Research Funds for the Central Universities (No. ZYGX2010J109)the Sichuan Youth Science and Technology Foundation (No. 2011JQ0003)
文摘In the present paper system and the solutions to the the solvability condition of the linearized Gauss-Codazzi homogenous system are given. In the meantime, the ＇solvability of a relevant linearized Darboux equation is given. The equations are arising in a geometric problem which is concerned with the realization of the Alexandrov＇s positive annulus in R^3.
基金This research is supported by the National 973 Program(2002CB312205).
文摘In this paper we examine controllability problems of evolution inclusions with nonlocal conditions. Using Kakutani's fixed point theorem and Schauder's fixed point the-orem, we establish sufficient conditions for the controllability under convex and nonconvex orientor fields respectively.
基金This research is partially supported by Key Laboratory of Management, Decision and Information Systems,CAS and National Science Foundations of China.
文摘This paper presents sensitivity analysis for parameterized variational inequality problems (VIP). Under appropriate assumption, it is shown that the perturbed solution to parameterized VIP is existent, unique, continuous and differentiable with respect to perturbation parameter. In the case of differentiability, we derive the equations for calculating the derivative of solution variables with respect to the perturbation parameters.
文摘The author introduces a concept of curvature bound set relative to second order impulsive differential systems and based on this concept discusses the existence of solutions to the Picard boundary value problem of the systems. Compared with the previous works finished by Lakshmikantham and Erbe, the author's results do not require the right handed function and impulsive functions with special structures such as monotonicity, etc. When the impulsive effects are absent, these results could be viewed as new generalized forms of the two so called optimal results about second order scalar differential equations derived by Lees and Mawhin respectively.
