Asymptotic stability and asymptotic solutions of second-order differential equations
نویسندگان
چکیده
منابع مشابه
Asymptotic stability and asymptotic solutions of second-order differential equations
We improve, simplify, and extend on quasi-linear case some results on asymptotical stability of ordinary second-order differential equations with complex-valued coefficients obtained in our previous paper [G.R. Hovhannisyan, Asymptotic stability for second-order differential equations with complex coefficients, Electron. J. Differential Equations 2004 (85) (2004) 1–20]. To prove asymptotic stab...
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I ■V *■ • • • iV*TC | V j j J j (1.1) x'=/(x) in which f(x) is of class C1 on En. Let J(x) = (df/dx) denote the Jacobian matrix of /and let H(x) = (J+J*)/2 be the symmetric part of J(x). One of the results of [2] is to the effect that if (1.2) /(0) = 0 and (1.3) H(x) is negative definite (for fixed x ^ 0), then x = 0 is a globally asymptotically stable solution of (1.1); i.e., every solution x ...
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An evolution problem for abstract differential equations is studied. The typical problem is: u̇ = A(t)u+F(t,u), t ≥ 0; u(0) = u0; u̇ = du dt (∗) Here A(t) is a linear bounded operator in a Hilbert spaceH, and F is a nonlinear operator, ‖F(t,u)‖≤ c0‖u‖, p > 1, c0, p = const > 0. It is assumed that Re(A(t)u,u) ≤ −γ(t)‖u‖2 ∀u ∈ H, where γ(t) > 0, and the case when limt→∞ γ(t) = 0 is also considered....
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2007
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2006.03.076