First and foremost, I would like to express my deepest and sincere gratitude to my supervisor, Prof. Guoqiang Hu, for his constant support, provoking suggestion and academic guidance before and during my PhD journey. As a mentor, he put a lot of effort into my work and helped me to be an independent researcher with professional skills. His dedication to research and the rigour in mathematics have a great influence on me. He also gave me many opportunities to practice myself which benefit me a lot for my future career planning and development. Thanks again for offering me the chance to study and do research here, which will be my best memories one day. Thanks to my committee members Prof. Lihua Xie and Prof. Jun Luo for their help and suggestion to my research. Thanks to Dr. Zhi Feng and Dr. Maojiao Ye for all the thoughtful discussions. Thanks to all my lab colleagues for their selfless help throughout my four years here. Lastly, thanks to my parents, for their support, encouragement, and also criticism, and all the efforts to make me happy.