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111.
EXACT CONTROLLABILITY FOR FIRST ORDER QUASILINEAR HYPERBOLIC SYSTEMS WITH ZERO EIGENVALUES*** 总被引:4,自引:0,他引:4
For a class of mixed initial-boundary value problem for general quasilinear hyperbolic sys-tems with zero eigenvalues, the authors establish the local exact controllability with boundary controls acting on one end or on two ends and internai controls acting on a part of equations in the system. 相似文献
112.
GLOBAL ASYMPTOTIC STABILITY IN N-SPECIES NONAUTONOMOUS LOTKA-VOLTERRACOMPETITIVE SYSTEMS WITH DELAYS
A delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solutions of the system. As a corollary, it is shown that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the delays are sufficiently small. 相似文献
113.
In this paper, we give the necessary and sufficient condition for the coexistence of a class of cubic curve separatrix cycles and limit cycles to the cubic system, and study their topological structures. 相似文献
114.
This paper uses the method of linear approximation for impulsive systems and gets a theorem which guarantees a fishery modei to be asymptotically stable at its equilibrium point and gives the ecological explanation. 相似文献
115.
In this paper we obtain some sufficient conditions for the existence of non-constant periodic solutions of the following planar system with six delaysOur approach is based on the continuation theorem of the coincidence degree. 相似文献
116.
Wen-junSun 《应用数学学报(英文版)》2003,19(1):143-156
This paper deals with the existence and nonexistence of global positive solution to a semilinear reaction-diffusion system with nonlinear boundary conditions.For the heat diffusion case,the necessary and sufficient conditions on the global existence of all positive solutions are obtained.For the general fast diffusion case,we get some conditions on the global existence and nonexistence of positive solutions.The results of this paper fill the some gaps which were left in this field. 相似文献
117.
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
118.
Hailiang Liu 《Journal of Differential Equations》2003,192(2):285-307
This paper studies the asymptotic stability of traveling relaxation shock profiles for hyperbolic systems of conservation laws. Under a stability condition of subcharacteristic type the large time relaxation dynamics on the level of shocks is shown to be determined by the equilibrium conservation laws. The proof is due to the energy principle, using the weighted norms, the interaction of waves from various modes is treated by imposing suitable weight matrix. 相似文献
119.
Liuman Ou Guilie Luo Yiping Li 《Journal of Mathematical Analysis and Applications》2003,283(2):534-548
In this paper, we consider an autonomous predator-prey Lotka-Volterra system in which individuals in the population may belong to one of two classes: the immatures and the matures, the age to maturity is represented by a time delay. By using eigenvalue analysis, principal term analyze method, reduction to absurdity, and iterative method, we obtain some simple conditions for global asymptotic stability of the unique positive equilibrium point. Moreover, a condition that the prey population in the system get extinction and the predator population in the system get permanence will be obtained. Meanwhile the theorems extend the corresponding conclusions in which there have no two stage structures. 相似文献
120.
It is well known that there is a planar sloop of cardinality n for each n≡2 or 4 (mod 6) (Math. Z. 111 (1969) 289–300). A semi-planar sloop is a simple sloop in which each triangle either generates the whole sloop or the 8-element sloop. In fact, Quackenbush (Canad. J. Math. 28 (1976) 1187–1198) has stated that there should be such semi-planar sloops. In this paper, we construct a semi-planar sloop of cardinality 2n for each n≡2 or 4 (mod 6). Consequently, we may say that there is a semi-planar sloop that is not planar of cardinality m for each m>16 and m≡4 or 8 (mod 12). Moreover, Quackenbush (Canad. J. Math. 28 (1976) 1187–1198) has proved that each finite simple planar sloop generates a variety, which covers the smallest non-trivial subvariety (the variety of all Boolean sloops) of the lattice of the subvarieties of all sloops. Similarly, it is easy to show that each finite semi-planar sloop generates another variety, which also covers the variety of all Boolean sloops. Furthermore, for any finite simple sloop
of cardinality n, the author (Beiträge Algebra Geom. 43 (2) (2002) 325–331) has constructed a subdirectly irreducible sloop
of cardinality 2n and containing
as the only proper normal subsloop. Accordingly, if
is a semi-planar sloop, then the variety
generated by
properly contains the subvariety
. 相似文献