An Abstract Existence Theorem at Resonance and Its Applications
An Abstract Existence Theorem at Resonance and Its Applications
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DOI：
10.1006/jdeq.1997.3397
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发表时间：
1998-05
影响因子：
2.4
通讯作者：
Shiwang Ma;Zhicheng Wang;Jianshe Yu
中科院分区：
文献类型：
--
作者：
Shiwang Ma;Zhicheng Wang;Jianshe Yu
摘要 利用布劳威尔度理论和基于莫欣重合度的连续定理，提出了算子方程共振时的抽象存在定理。作为这一结果的应用，给出了共振半线性方程周期解存在的一些充分条件，其中线性部分的核具有维数N（N⩾2）。 Nagle 和 Sinkala 的结果得到了推广、改进和统一。
Abstract By using Brouwer degree theory and a continuation theorem based on Mawhin's coincidence degree, an abstract existence theorem at resonance for operator equations is developed. As applications of this result, some sufficient conditions are given for the existence of periodic solutions of semilinear equations at resonance where the kernel of the linear part has dimension N ( N ⩾2). The results due to Nagle and Sinkala are generalized, improved, and unified.