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Table of Content
30 December 2019, Volume 34 Issue 4
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Well-posedness for A Plat Equations with Nonlocal Source Term
LIU Gong-wei, ZHAO Rui-min, ZHANG Hong-wei
2019, 34(4): 331-342. doi:
10.13371/j.cnki.chin.q.j.m.2019.04.001
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In this paper,we investigate the initial boundary value problem for a plate equation with nonlocal source term.The local,global existence and exponential decay result are established under certain conditions.Moreover,we also prove the blow-up in finite time and the lifespan of solution under certain conditions.
On Products and Diagonal of Mappings in Generalized Topological Space
CAO Chun-fang, SHEN Rong-xin
2019, 34(4): 343-351. doi:
10.13371/j.cnki.chin.q.j.m.2019.04.002
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Based on the theory of products of generalized topologies,we introduce the product mappings and the diagonal mappings in generalized topological spaces in this paper.We investigate some basic properties(especially,the continuity,openness and closedness) of the product mappings and the diagonal mappings in generalized topological spaces.Some applications are given to answer two questions raised in [3].
Global Existence of Solutions to The Keller-Segal System with Initial Data of Large Mass
SHEN Ren-kun
2019, 34(4): 352-361. doi:
10.13371/j.cnki.chin.q.j.m.2019.04.003
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In this paper,the Cauchy problem of the classical Keller-Segel chemotaxis model with initial data of large mass is considered.By the Green’s function method and scaling technique,we prove that if‖u
0
‖■‖u
0
‖■ and κ‖Δv
0
‖Lp are less than some constant,then the problem always admits a unique global classical solution,even when the initial mass‖u
0
‖L
1
is large.Moreover,the decay rates of the classical solution are also obtained.
Some Random Coincidence Point and Common Fixed Point Results in Cone Metric Space Over Banach Algebras
JIANG Bing-hua, CAI Ze-lin, CHEN Jin-yang
2019, 34(4): 362-381. doi:
10.13371/j.cnki.chin.q.j.m.2019.04.004
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In this paper,we obtain some tripled common random fixed point and tripled random fixed point theorems with several generalized Lipschitz constants in such spaces.We consider the obtained assertions without the assumption of normality of cones.The presented results generalize some coupled common fixed point theorems in the existing literature.
Existence and Multiplicity of Periodic Solutions for The Non-autonomous Second-order Hamiltonian Systems
CHEN Yu-song, CHANG He-jie
2019, 34(4): 382-396. doi:
10.13371/j.cnki.chin.q.j.m.2019.04.005
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In this paper,we study the existence and multiplicity of periodic solutions of the non-autonomous second-order Hamiltonian systems■where T> 0.Under suitable assumptions on F,some new existence and multiplicity theorems are obtained by using the least action principle and minimax methods in critical point theory.
Global Stability of An Eco-epidemiological Model with Beddington-DeAngelis Functional Response and Delay
BAI Hong-fang, XU Rui
2019, 34(4): 397-409. doi:
10.13371/j.cnki.chin.q.j.m.2019.04.006
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In this paper,an eco-epidemiological model with Beddington-DeAngelis functional response and a time delay representing the gestation period of the predator is studied.By means of Lyapunov functionals and Laselle’s invariance principle,sufficient conditions are obtained for the global stability of the interior equilibrium and the disease-free equilibrium of the system,respectively.
Asymptotic Behavior for A Class of Non-autonomous Nonclassical Parabolic Equations with Delay on Unbounded Domain
ZHANG Fang-hong, BAI Li-hong
2019, 34(4): 410-430. doi:
10.13371/j.cnki.chin.q.j.m.2019.04.007
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In this article,we investigate the longtime behavior for the following non autonomous nonclassical parabolic equations on unbounded domain u
t
-△u
t
-△u+λu=f（x,u（x,t-ρ（t）））+g（x,t）Under some suitable conditions on the delay term f and the non-autonomous forcing term g,we prove the existence of uniform attractors in Banach space C
H
1
（R
N
）
for the multivalued process generated by non-autonomous nonclassical parabolic equations with delays in unbounded domain.
Research on Robust Cooperative Dual Equilibrium with Ellipsoidal Asymmetric Strategy Uncertainty
LUO Gui-mei
2019, 34(4): 431-440. doi:
10.13371/j.cnki.chin.q.j.m.2019.04.008
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In this paper,we investigate robust cooperative dual equilibria with two players in which each player minimizes the opponent’s cost and can not evaluate his own strategy while may estimate an asymmetric bounded set of the mixed strategy.Using dual theory and robust optimization technique,we obtain a result that the counterpart of the primitive uncertainty with ellipsoidal norm for each player can be formulated as a second-order cone programming(SOCP) and solving the corresponding equilibrium can be converted to solving a second-order cone complementarity problem(SOCCP).Then we present a numerical experiment to illustrate the behavior of robust cooperative dual equilibrium.
