Periodic solutions of systems with asymptotically evennonlinearities

Peter E.Kloeden; Alexander M.Krasnoselskii

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Periodic solutions of systems with asymptotically evennonlinearities

机译：渐近偶非线性系统的周期解

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New conditions of solvability based on a general theorem on the calculation of the index at infinity for vector fields that have degenerate principal linear part as well as degenerate “next order” terms are obtained for the2π-periodic problem for the scalar equationx″+n2x=g(|x|)+f(t,x)+b(t)with boundedg(u)andf(t,x)→0as|x|→0. The result is also applied to the solvability of a two-point boundary value problem and to resonant problems for equations arising in control theory.

机译：对于标量方程x''+ n2x =的2π周期问题，获得了具有一般主定理的无穷大新解的条件，该定理基于无穷大主线性部分以及退化“ n阶”项的矢量场的无穷大索引的计算。 g（| x |）+ f（t，x）+ b（t）有界g（u）和f（t，x）→0as | x |→0。该结果还适用于两点边值问题的可解性以及控制理论中出现的方程的共振问题。

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《International journal of stochastic analysis》 |2000年第1期|共10页
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Peter E.Kloeden; Alexander M.Krasnoselskii;
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Periodic solutions of systems with asymptotically evennonlinearities

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