He had to rely on whatever books were lying around.
He knew nothing whatever about it.
There is no scientific evidence whatever to support such a view.
句（1），感觉好别扭，不知该如何断句和理解？
句（2）（3）里，介词汇短语前都多了个whatever，该如何理解句子的意思，还是定语吗？
He had to rely on whatever books were lying around.
He knew nothing whatever about it.
There is no scientific evidence whatever to support such a view.
以上三句都正确。
句（1）whatever 是融合型关系限定词，引导名词性关系分句。whatever 没疑问含义。分句等于一个名词词组。
whatever books were lying around = any books thatwere lying around （任何在周围的书本）
句（2）和（3）whatever 是用来强调否定的副词，意为“任何；丝毫”。用于名词性词组（包含不定代词）后，强调否定陈述。跟 at all 的使用方法类似，可以省去。
He knew nothing about it.
There is no scientific evidence to support such a view.
【翻译】
（1）他不能不依赖阅读身边周围的书本。
（2）他对此一无所知
（3）没任何证据表明，广播业的角逐使本钱有所减少。