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941.
The theory of monotone semiflows has been widely applied to functional differential equations (FDEs). The studies on the theory and applications of monotone semiflows for FDEs are very important and interesting. A brief des-cription of our recent works are as follows.By using general monotone semiflow theory, several results of positively invariant sets, monotone solutions and contracting rectangles of retarded functional differential equations(RFDEs) with infinite delay are gained under the assumption of quasimonotonicity; sufficient conditions for the existence, un-iqueness and global attractivity of periodic solutions are also established by combining the theory of monotone semiflows for neutral functional differential equations(NFDEs) and Krasnoselskii's fixed point theorem. 相似文献
942.
Sufficient conditions are established for the asymptotic behavior of solutionsof nonlinear delay differential equations x′(t)+sum from i=1 to m(pi(t)x(t-т_i))=F(t,x_t),t≥0where 0<т_1<т_2<…<т_m≤r,pi∈C([0,∞)),i=1,2,…,m,F∈C([0,∞)×C_0,R).C_0=C([-r,0],R)equipped with the sup norm ||·|| forsome r>0. A new result is established, some known results are improved. 相似文献
943.
Zheng-qiu Zhang Xian-wu Zeng Zhi-cheng WangCollege of Mathematics Wuhan University Wuhan . China College of Mathematics. Hunan University Changsha China 《应用数学学报(英文版)》2003,19(4):691-702
Abstract By using the continuation theorem of coincidence degree theory,the existence of a positive periodicsolution for a nonautonomous diffusive food chain system of three species. dx_1(t)/dt=x_1(t)[r_1(t)-a_(11)(t)x_1(t)-a_(12)(t)x_2(t)]+D_1(t)[y(t)-x_1(t)], dx_2(t)/dt=x_2(t)[-r_2(t)+a_(21)(t)x_1(t-r_1)-a_(22)(t)x_2(t)-a_(23)(t)x_3(t)], dx_3(t)/dt=x_3(t)[-r_3(t)+a_(32)(t)x_2(t-r_2)-a_(33)(t)x_3(t)], dy(t)/dt=y(t)[r_4(t)-a_(44)(t)y(t)]+D_2(t)[x_1(t)-y(t)]+D_2(t)[x_1(t)-y(t)],is established,where,r_i(t),a_(ii)(t)(i=1,2,3,4),D_i(t)(i=1,2),a_(12)(t),a_(21)(t),a_(23)(t)and a_(32)(t) are all positiveperiodic continuous functions with period w>0,T_i(i=1,2)are positive constants. 相似文献
944.
For a class of quasilinear Schrödinger equations, we establish the existence of ground states of soliton-type solutions by a variational method. 相似文献
945.
For the minimal surfaces in Rn with Plateau boundary condition and establish the global existence and uniqueness of the flow as well as the continuous dependence of the initial datum. 相似文献
946.
Boris S. Mordukhovich Bingwu Wang 《Journal of Mathematical Analysis and Applications》2003,282(1):63-84
In this paper we study some properties of sets, set-valued mappings, and extended-real-valued functions unified under the name of “sequential normal compactness.” These properties automatically hold in finite-dimensional spaces, while they play a major role in infinite-dimensional variational analysis. In particular, they are essential for calculus rules involving generalized differential constructions, for stability and metric regularity results and their broad applications, for necessary optimality conditions in constrained optimization and optimal control, etc. This paper contains principal results ensuring the preservation of sequential normal compactness properties under various operations over sets, set-valued mappings, and functions. 相似文献
947.
Let f(z) be a normalized convex (starlike) function on the unit disc D. Let , where z=(z1,z2,…,zn), z1∈D, , pi?1, i=2,…,n, are real numbers. In this note, we prove that Φ(f)(z)=(f(z1),f′(z1)1/p2z2,…,f′(z1)1/pnzn) is a normalized convex (starlike) mapping on Ω, where we choose the power function such that (f′(z1))1/pi|z1=0=1, i=2,…,n. Some other related results are proved. 相似文献
948.
This paper studies the following two-dimensional nonlinear partial difference systems
949.
In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second-order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in Proc. London Math. Soc. 63 (1991) 212-240 and Comm. Partial Differential Equations 16 (1991) 1095-1128. 相似文献
950.
In this paper, we establish existence results for positive solutions for the (n−1,1) three-point boundary value problems consisting of the equation