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91.
92.
Luis Barreira Meng Fan Claudia Valls Jimin Zhang 《Nonlinear Analysis: Theory, Methods & Applications》2012
We establish the existence of Lipschitz stable invariant manifolds for semiflows generated by a delay equation x′=L(t)xt+f(t,xt,λ), assuming that the linear equation x′=L(t)xt admits a nonuniform exponential dichotomy and that f is a sufficiently small Lipschitz perturbation. We also show that the stable invariant manifolds are Lipschitz in the parameter λ. 相似文献
93.
94.
Luis Barreira Meng Fan Claudia Valls Jimin Zhang 《Journal of Dynamics and Differential Equations》2012,24(1):101-118
We establish the existence of Lipschitz stable invariant manifolds for semiflows generated by a delay equation x′ = L(t)x
t
+ f (t, x
t
, λ), assuming that the linear equation x′ = L(t)x
t
admits a polynomial dichotomy and that f is a sufficiently small Lipschitz perturbation. Moreover, we show that the stable invariant manifolds are Lipschitz in the
parameter λ. We also consider the general case of nonuniform polynomial dichotomies. 相似文献
95.
We classify new classes of centers and of isochronous centers for polynomial differential systems in
\mathbb R2{\mathbb R^2} of arbitrary odd degree d ≥ 7 that in complex notation z = x + i
y can be written as
[(z)\dot] = (l+i) z + (z[`(z)])\fracd-7-2j2 (A z5+j[`(z)]2+j + B z4+j[`(z)]3+j + C z3+j[`(z)]4+j+D[`(z)]7+2j ),\dot z = (\lambda+i) z + (z \overline z)^{\frac{d-7-2j}2} \left(A z^{5+j} \overline z^{2+j} + B z^{4+j} \overline z^{3+j} + C z^{3+j} \overline z^{4+j}+D \overline z^{7+2j} \right), 相似文献
96.
For impulsive differential equations, we establish the existence of invariant stable manifolds under sufficiently small perturbations of a linear equation. We consider the general case of nonautonomous equations for which the linear part has a nonuniform exponential dichotomy. One of the main advantages of our work is that our results are optimal, in the sense that for vector fields of class C 1 outside the jumping times, we show that the invariant manifolds are also of class C 1 outside these times. The novelty of our proof is the use of the fiber contraction principle to establish the smoothness of the invariant manifolds. In addition, using the same approach we can also consider linear perturbations. 相似文献
97.
98.
99.
100.
This review deals with the stereoselective formation of organic compounds. A number of examples of such syntheses, especially those of alkaloids and steroids, are described. An asymmetric synthesis, which avoids the intricacies and wastefulness of optical resolution, has been successful in a few cases only. The procedures of configurational change and of optical resolution, as well as the planning of multi-step stereoselective syntheses, are discussed. 相似文献
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