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In this paper, we study the existence of nontrivial homoclinic orbits of a dynamic equation on time scales T of the formWe construct a variational framework of the above-mentioned problem, and some new results on the existence of a homoclinic orbit or an unbounded sequence of homoclinic orbits are obtained by using the mountain pass lemma and the symmetric mountain pass lemma, respectively. The interesting thing is that the variational method and the critical point theory are used in this paper. It is notable that in our study any periodicity assumptions on p(t), q(t) and f (t, u) are not required.

In order to improve the accuracy of video image moving target recognition and shorten the recognition time, a video image moving target recognition method based on a generation countermeasure network is proposed. Firstly, the image sensor is used to collect the video image and obtain the video image sequence. The Roberts operator is used for edge detection and Gaussian smoothing of the video image. Secondly, the normalization method is used to extract the key features of moving targets in video images. Finally, training is carried out alternately to generate the countermeasure network model, and the video image moving target recognition sample results are output according to the training results to realize the video image moving target recognition. The experimental results show that the highest recognition accuracy of the proposed method is 98.1%, and the longest recognition time is only 5.7 s, indicating that its recognition effect is good.