This paper considers the approximate controllability for a class of abstract semilinear control systems using a method called surjectivity theorems for nonlinear operator equations under restrictive assumptions. The sufficient conditions for approximate controllability are derived under the natural assumptions on the nonlinear terms, which is an odd homogeneous and the nonlinear inverse considered as a multivalued mapping is bounded. An example is given to illustrate our main results.

中文翻译：

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具有齐次性质的抽象半线性控制系统的可控性

本文考虑了一类抽象半线性控制系统的近似可控性，该方法使用一种称为满射性定理的方法，用于限制性假设下的非线性算子方程。近似可控性的充分条件是在非线性项的自然假设下导出的，非线性项是奇齐次的，并且被认为是多值映射的非线性逆是有界的。举一个例子来说明我们的主要结果。