共查询到20条相似文献,搜索用时 15 毫秒
1.
Stanislav Shkarin 《Mathematische Nachrichten》2003,257(1):87-98
Let X be a real Banach space, ω : [0, +∞) → ? be an increasing continuous function such that ω(0) = 0 and ω(t + s) ≤ ω(t) + ω(s) for all t, s ∈ [0, +∞). According to the infinite dimensional analog of the Osgood theorem if ∫10 (ω(t))?1 dt = ∞, then for any (t0, x0) ∈ ?×X and any continuous map f : ?×X → X such that ∥f(t, x) – f(t, y)∥ ≤ ω(∥x – y∥) for all t ∈ ?, x, y ∈ X, the Cauchy problem (t) = f(t, x(t)), x(t0) = x0 has a unique solution in a neighborhood of t0. We prove that if X has a complemented subspace with an unconditional Schauder basis and ∫10 (ω(t))?1 dt < ∞ then there exists a continuous map f : ? × X → X such that ∥f(t, x) – f(t, y)∥ ≤ ω(∥x – y∥) for all (t, x, y) ∈ ? × X × X and the Cauchy problem (t) = f(t, x(t)), x(t0) = x0 has no solutions in any interval of the real line. 相似文献
2.
Jan Jankowski 《Rendiconti del Circolo Matematico di Palermo》2006,55(1):95-102
We show the existence of absolutely continuous extremal solutions to the problemx′(t)=f(t, x)h(t)))+g(t)),x(0)=x
0, whereh is an arbitrary continuous deviated argument. Conditions for the uniqueness of solutions are given.
Research partialy supported by grant UG BW 5100 - 5 - 0143 - 4 相似文献
3.
Bingwen Liu 《Mathematische Nachrichten》2009,282(4):581-590
In this paper, we use the coincidence degree theory to establish new results on the existence and uniqueness of T ‐periodic solutions for a class of nonlinear n ‐th order differential equations with delays of the form x(n)(t) + f (x(n‐ 1)(t)) + g (t, x (t ‐ τ (t))) = p (t). 相似文献
4.
Qiyi Fan Wentao Wang Xuejun Yi 《Journal of Computational and Applied Mathematics》2009,230(2):762-769
In this paper, we use the Leray–Schauder degree theory to establish new results on the existence and uniqueness of anti-periodic solutions for a class of nonlinear nth-order differential equations with delays of the form
x(n)(t)+f(t,x(n−1)(t))+g(t,x(t−τ(t)))=e(t).