Hammerstein型夹杂的可解性
Solvability of inclusions of Hammerstein type
摘要：
对所谓的容许多重映射类给出了一个相当一般的Leray-Schauder型延拓定理。然后利用这个结果建立了求解Lebesgue-Bochner空间中Hammerstein型算子包含的一个普遍规则。例子包括$m$ -增生多值微分方程的扰动初值问题、半线性微分包含的反周期问题、Fredholm和Volterra型抽象积分包含以及非线性发展包含的两点边值问题.
英文摘要：
A fairly general continuation theorem of Leray-Schauder type for the class of so-called admissible multimaps is set forth. This result is then used to establish a universal rule for solving operator inclusions of Hammerstein type in Lebesgue-Bochner spaces. Examples illustrating the legitimacy of this approach include the initial value problem for perturbation of $m$-accretive mutivalued differential equations, the anti-periodic problem for semilinear differential inclusions, abstract integral inclusions of Fredholm and Volterra type and the two-point boundary value problem for nonlinear evolution inclusions.
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