弱导数与弱解的一个注记

A Note on Weak Derivative and Weak Solution

运用实际例子给出弱导数和弱解的一点注记,深化分部积分法在定积分中的实际运用,一方面根据定义验证弱解不一定有一阶连续偏导数,另一方面通过变号解的存在性获得更多解的存在性,在边值问题解的存在性与多重性研究中具有一定的价值,给变分问题的研究提供一定的参考.

A note on weak derivative and weak solution is given by practical examples and the practical application of the method of integration by parts is deepened in definite integration.For the results,we get that the weak solutions do not necessarily have first-order continuous partial derivatives according to the definition,and it is valuable that we can obtain the existence of multiple solutions by a sign-changing solution to boundary value problems.The conclusion is useful to some references for the study of variational problems.