We consider a system of neutral equations with unbounded delay, and derive conditions on Liapunov functionals to ensure that the solutions are uniformly bounded and uniformly ultimately bounded.
We consider the neutral functional differential equation(NFDE)with infinite delayd/dt D_x_t=f(t,x_t) and the neutral Volterra integro-differential equation ■ where x∈R^n, f: R×B→R^n is continuous, B is a given...We consider the neutral functional differential equation(NFDE)with infinite delayd/dt D_x_t=f(t,x_t) and the neutral Volterra integro-differential equation ■ where x∈R^n, f: R×B→R^n is continuous, B is a given phase space, D: B→R^n is a linear and continuous function, A, C, E are continuous functions.展开更多
Boltzmann equation is an equation which is related to the three variables of x, v, t. In this paper, we mainly study the space-uniform Boltzmann equation which unknown function F is not related to the position variabl...Boltzmann equation is an equation which is related to the three variables of x, v, t. In this paper, we mainly study the space-uniform Boltzmann equation which unknown function F is not related to the position variable x. We mainly use the contraction mapping theorem to find the existence of the solution, so our mainly work is to prove the self-mapping, i.e. to prove its uniformly bounded, and then to prove the contraction mapping. There we can get the range of ||B(θ)||L1(L∞), next we can figure out the range of M and T from the conditions what we know. Finally, from these conditions, we can find the existence of the solution.展开更多
文摘We consider a system of neutral equations with unbounded delay, and derive conditions on Liapunov functionals to ensure that the solutions are uniformly bounded and uniformly ultimately bounded.
文摘We consider the neutral functional differential equation(NFDE)with infinite delayd/dt D_x_t=f(t,x_t) and the neutral Volterra integro-differential equation ■ where x∈R^n, f: R×B→R^n is continuous, B is a given phase space, D: B→R^n is a linear and continuous function, A, C, E are continuous functions.
文摘Boltzmann equation is an equation which is related to the three variables of x, v, t. In this paper, we mainly study the space-uniform Boltzmann equation which unknown function F is not related to the position variable x. We mainly use the contraction mapping theorem to find the existence of the solution, so our mainly work is to prove the self-mapping, i.e. to prove its uniformly bounded, and then to prove the contraction mapping. There we can get the range of ||B(θ)||L1(L∞), next we can figure out the range of M and T from the conditions what we know. Finally, from these conditions, we can find the existence of the solution.
