Under the pressures of population aging and new urbanization, enhancing the well-being of the elderly has become an effective measure to ensure the sustainable development of large cities. Using the 13 counties and districts of Xi'an as the research unit, an evaluation index system for elderly well-being was constructed across four dimensions, including material, health, spiritual, and social. Combining the Analytic Hierarchy Process (AHP) and the Criticality Weighting Method (CRITIC) to measure the well-being levels of the elderly across these 13 counties and districts. The obstacle degree model was employed to identify the key obstacle factors on the elderly well-being. The research results reveal 4 findings. ① Gaoling District exhibits the highest overall elderly welfare, while Baqiao District ranks lowest. The four dimensions rank from highest to lowest as material life, spiritual life, social life, and health life. ② The spatial distribution of well-being exhibits higher levels in the north and south, while lower levels were observed in the east and west. Areas with higher levels were concentrated in northern counties and southern counties of the main urban area, while lower levels were clustered in the eastern and western peripheries. ③ The main obstacle factors to the well-being of the elderly in Xi'an include the source of daily necessities and the total monthly income in the material life dimension, health status and satisfaction with medical insurance reimbursement in the healthy life dimension, the frequency of participation in tourism activities in the spiritual life dimension, and the availability of supporting parks in the social life dimension. ④ Based on differences in these obstacle factors, the counties and districts in the study area can be classified into areas where elderly income needs to be increased, areas where medical security needs to be optimized, and areas where public facilities need to be improved.

On the basis of the fifth, sixth and seventh national population census data, we identify the shrinking cities in the Yellow River Basin and measure their shrinkage intensity. The multi-index comprehensive evaluation method and the coupling coordination model were used to analyze the size of the "production-living-ecological" functions and the coupling coordination scheduling of shrinking cities in 2010, 2015 and 2020. We also use the random forest model to explore its key influencing factors. The results show that among the 90 prefecture-level cities（stages and leagues） in the Yellow River Basin, there are 27 continuous contracting cities, 9 stage contracting cities and 29 potential contracting cities. The phenomenon of urban contraction is significant. During the study period, the production and living functions of the shrinking cities in the Basin were on the rise as a whole, and the level of "production-living-ecological" functions in different regions was significantly different. The coupling coordination degree of the shrinking cities' "production-living-ecological" functions was characterized by the development from barely coordinated to primary coordinated development. The coordination degree of the middle and lower reaches was better than that of the upper reaches. The development of economic society and the improvement of people's living standards contributed to the coupling and coordinated development of the "production-living-ecological" functions.