共查询到20条相似文献,搜索用时 15 毫秒
1.
Svatoslav Staněk 《Computers & Mathematics with Applications》2011,62(3):1379-1388
We discuss the existence of positive solutions for the singular fractional boundary value problem Dαu+f(t,u,u′,Dμu)=0, u(0)=0, u′(0)=u′(1)=0, where 2<α<3, 0<μ<1. Here Dα is the standard Riemann-Liouville fractional derivative of order α, f is a Carathéodory function and f(t,x,y,z) is singular at the value 0 of its arguments x,y,z. 相似文献
2.
The paper is devoted to the study of the homogeneous Dirichlet problem for the doubly nonlinear parabolic equation with nonstandard growth conditions:
ut=div(a(x,t,u)|u|α(x,t)|∇u|p(x,t)−2∇u)+f(x,t) 相似文献
3.
We consider a nonlinear discrete-time system of the form Σ: x(t+1)=f(x(t), u(t)), y(t) =h(x(t)), where x ε RN, u ε Rm, y ε Rq and f and h are analytic. Necessary and sufficient conditions for local input-output linearizability are given. We show that these conditions are also sufficient for a formal solution to the global input-output linearization problem. Finally, we show that zeros at infinity of ε can be obtained by the structure algorithm for locally input-output linearizable systems. 相似文献
4.
《国际计算机数学杂志》2012,89(10):2259-2267
We formulate a new alternating direction implicit compact scheme of O(τ2+h 4) for the linear hyperbolic equation u tt +2α u t +β2 u=u xx +u yy +f(x, y, t), 0<x, y<1, 0<t≤T, subject to appropriate initial and Dirichlet boundary conditions, where α>0 and β≥0 are real numbers. In this article, we show the method is unconditionally stable by the Von Neumann method. At last, numerical demonstrations are given to illustrate our result. 相似文献
5.
A new representation is proved of the solutions of initial boundary value problems for the equation of the form u xx (x, t) + r(x)u x (x, t) ? q(x)u(x, t) = u tt (x, t) + μ(x)u t (x, t) in the section (under boundary conditions of the 1st, 2nd, or 3rd type in any combination). This representation has the form of the Riemann integral dependent on the x and t over the given section. 相似文献
6.
Qiaoshun Yang Zhiting Xu 《Computers & Mathematics with Applications》2011,62(10):3682-3691
In this paper, we consider the second-order quasilinear neutral dynamic equation
(r(t)|ZΔ(t)|α−1ZΔ(t))Δ+q(t)|x(δ(t))|β−1x(δ(t))=0, 相似文献
7.
《Computers & Mathematics with Applications》2003,45(6-9):873-885
A double fixed-point theorem is applied to obtain the existence of at least two positive solutions for the boundary value problem, (−1)my(2m)(t) = f(y(t)), t ϵ [0, 1], y(2i)(0) = y(2i+1)(1) = 0, 0 ≤ i ≤ m−1. It is later applied to obtain the existence of at least two positive solutions for the analogous discrete boundary value problem, (−1)mΔ2mu(k) = g(u(k)), k ϵ {0, …, N}, Δ2iu(0) = Δ2i+1u(N + 1) = 0, 0 ⩽ m − 1. 相似文献
8.
《Computers & Mathematics with Applications》2001,41(5-6):689-696
This paper deals with diffusion problems modeled by the equation a(t)uxx = ut, x > 0, t > 0, u(x, 0) = c(x) together with the boundary condition u(0, t) = b(t) or ux(0, t) = b(t). By using Fourier transforms, existence conditions and exact solutions of the above mixed problems are given. 相似文献
9.
For 0≤x≤1, 0≤t≤T we consider the diffusion equation $$\gamma (x)u_t (x, t) - (B u)_x (x, t) = f(x, t)$$ with (alternatively)B u:=(a(x)u) x +b(x)u ora(x)u x +β(x)u. There are given initial valuesu(x,0), influx rates?(B u) (0,t) and (B u) (1,t) across the lateral boundaries and an influx rate (B u) (ζ?0,t)?(B u) (ζ+0,t) at an interface ζ∈(0, 1) where the elsewhere smooth functions γ,a, b, β are allowed to have jump discontinuities.a and γ are assumed to be positive. Interpretingu(x, t) as temperature and γ(x) u (x, t) as energy density we can easily express the total energy \(E(t) = \int\limits_0^1 {\gamma (x) u (x, t)} \) in terms of integrals of the given data. We describe and analyse explicit and implicit one-step difference schemes which possess a discrete quadrature analogue exactly matchingE(t) at the time grid points. These schemes also imitate the isotonic dependence of the solution on the data. Hence stability can be proved by Gerschgorin's method and, under appropriate smoothness assumptions, convergence is 0 ((Δx)2+Δt). 相似文献
10.
Y. Ling 《Computing》1997,58(3):295-301
In this paper an improved Moore test for the coupled system:f(x, y)=0,g(x, y)=0 is described: x+ is calculated from x and y in a forward-substep, and we use x+ and y to compute y+ in a backward-substep. It is shown that, if x+ ? x, y+ ? y, then a solution of the coupled system (x*,y*) ∈ (x+, y+) exists. On this foundation, we prove convergence of a point iterative algorithm for solving coupled systems. 相似文献
11.
Fabrizio Durante 《Information Sciences》2009,179(15):2689-223
A semi-copula S:[0,1]2→[0,1] is called supermigrative if it is commutative and satisfies S(αx,y)?S(x,αy) for all α∈[0,1] and for all x,y∈[0,1] such that y?x. In this paper, the class of supermigrative semi-copulas is investigated, by focusing, in particular, on the subclass of continuous triangular norms. Some interesting connections with the theory of copulas are also underlined. 相似文献
12.
This paper is concerned with the nonlinear partial difference equation with continuous variables,where a, σi, τi are positive numbers, hi(x, y, u) ε C(R+ × R+ × R, R), uhi(x, y, u) > 0 for u ≠ 0, hi is nondecreasing in u, i = 1, …, m. Some oscillation criteria of this equation are obtained. 相似文献
13.
Chanying Li Author Vitae Author Vitae 《Automatica》2010,46(6):999-1007
It is fairly well known that there are fundamental differences between adaptive control of continuous-time and discrete-time nonlinear systems. In fact, even for the seemingly simple single-input single-output control system yt+1=θ1f(yt)+ut+wt+1 with a scalar unknown parameter θ1 and noise disturbance {wt}, and with a known function f(⋅) having possible nonlinear growth rate characterized by |f(x)|=Θ(|x|b) with b≥1, the necessary and sufficient condition for the system to be globally stabilizable by adaptive feedback is b<4. This was first found and proved by Guo (1997) for the Gaussian white noise case, and then proved by Li and Xie (2006) for the bounded noise case. Subsequently, a number of other types of “critical values” and “impossibility theorems” on the maximum capability of adaptive feedback were also found, mainly for systems with known control parameter as in the above model. In this paper, we will study the above basic model again but with additional unknown control parameter θ2, i.e., ut is replaced by θ2ut in the above model. Interestingly, it turns out that the system is globally stabilizable if and only ifb<3. This is a new critical theorem for adaptive nonlinear stabilization, which has meaningful implications for the control of more general uncertain nonlinear systems. 相似文献
14.
We present some new results about oscillation and asymptotic behavior of solutions of third order nonlinear differential equations of the form
(r2(t)(r1(t)y′)′)′+p(t)y′+q(t)f(y(g(t)))=0. 相似文献
15.
In this paper the quasilinear heat equation with the nonlinear boundary condition is studied. The blow-up rate and existence of a self-similar solution are obtained. It is proved that the rescaled function
v(y,t)=(T−t)1/(2p+α−2)u((T−t)(p−1)/(2p+α−2)y,t),