Bounded solutions of nonlinear Cauchy problems

JosefKreulich

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Bounded solutions of nonlinear Cauchy problems

机译：非线性柯西问题的有界解

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For a given closed and translation invariant subspaceYof the bounded and uniformly continuous functions, we will give criteria for the existence of solutionsu∈Yto the equationu′(t)+A(u(t))+ωu(t)?f(t),t∈?, or of solutionsuasymptotically close toYfor the inhomogeneous differential equationu′(t)+A(u(t))+ωu(t)?f(t),t>0,u(0)=u0, in general Banach spaces, whereAdenotes a possibly nonlinear accretive generator of a semigroup. Particular examples for the spaceYare spaces of functions with various almost periodicityproperties and more general types of asymptotic behavior.

机译：对于给定的有界且一致连续函数的闭合平移不变子空间Y，我们将给出方程u′（t）+ A（u（t））+ωu（t）？f（t）的解u∈Y存在性的判据，t∈?,或者对于非齐次微分方程u′（t）+ A（u（t））+ωu（t）？f（t），t> 0，u（0）= u0通常近似于Y的解Banach空间，其中A表示半群的可能的非线性增生生成器。具有各种几乎周期性属性和渐近行为的更一般类型的函数spaceYare空间的特定示例。

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《Abstract and applied analysis》 |2002年第12期|共25页
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JosefKreulich;
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机译：非线性Cauchy问题的有界解

Bounded solutions of nonlinear Cauchy problems

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