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This study investigates existence result of a nontrivial weak solutions for a system of nonlinear elliptic equations involving Hardy Potentials. The problem arises in the mathematical modeling of complex physical phenomena.

The study examines the digital finance (DF) and regional sustainable development (RSD) across 90 cities within six major city clusters in China over the period from 2011 to 2020. By constructing an evaluation index system for DF and RSD, we employed the entropy value method to assess their levels, and the coupling coordination degree (CCD) model to evaluate their interplay. Our analysis extended to temporal and spatial disparities, distribution dynamics, and the convergence of CCD through kernel density estimation, Markov chain analysis, σ -convergence, and β -convergence techniques. The results indicate a consistent upward trend in CCD, yet it remains at a low level with pronounced regional disparities and temporal characteristics. The kernel density distribution’s central tendency has shifted rightward progressively, albeit with a decelerating pace annually. The Markov transition probability matrix suggests a stable CCD across various levels, hinting at “club convergence”. Furthermore, both σ -convergence and β -convergence analyses reveal significant convergence trends in CCD, enhanced by economic growth factors. Using the Quadratic Assignment Procedure (QAP) method, we found that regional economic growth disparities significantly influence the CCD’s regional variances.

In the current global context, digital finance (DF) and sustainable economic development (SED) are important topics. The synergies between DF and SED have already been proven. However, the measurement and quantitative analysis of the coupling coordination degree (CCD) of DF and SED have not received sufficient attention to date. Based on data from 55 cities in the Yellow River Basin (YRB) from 2011 to 2021, this study constructs an evaluation index system of DF and SED and measures their level, respectively. The proposed CCD model is then used to measure the CCD between the two systems. In addition, kernel density estimation, Markov chain, σ -convergence, β -convergence, and the quadratic assignment procedure (QAP) method are used to study the spatial pattern, distribution dynamic evolution trend, convergence, and influencing factors of the regional differences in the CCD. The results show that: (1) From 2011 to 2021, the CCD level showed a stable upward trend and regional heterogeneity, and the time stage characteristics were more obvious. (2) The center position and change interval of the overall distribution curve of the kernel density estimation gradually shifted to the right. The Markov transfer probability matrix shows that the CCD is more stable among different levels, indicating a phenomenon of “club convergence”. (3) A convergence analysis shows that there are significant σ -convergence, absolute β -convergence, and conditional β -convergence. (4) The QAP regression shows that factors such as the regional differences in GDP per capita have a significant impact on the regional differences in the CCD. This study offers a comprehensive structure that can be used to examine the synergistic effects between DF and SED; the research findings can also provide perspectives for other areas.

Grey models have attracted considerable attention as a time series forecasting tool in recent years. Nevertheless, the linear characteristics of the differential equations on which traditional grey models rely frequently result in inadequate predictive accuracy and applicability when addressing intricate nonlinear systems. This study introduces a conformable fractional order unbiased kernel-regularized nonhomogeneous grey model (CFUKRNGM) based on statistical learning theory to address these limitations. The proposed model initially uses a conformable fractional-order accumulation operator to derive distribution information from historical data. A novel regularization problem is then formulated, thereby eliminating the bias term from the kernel-regularized nonhomogeneous grey model (KRNGM). The parameter estimation of the CFUKRNGM model requires solving a linear equation with a lower order than the KRNGM model, and is automatically calibrated through the Bayesian optimization algorithm. Experimental results show that the CFUKRNGM model achieves superior prediction accuracy and greater generalization performance compared to both the KRNGM and traditional grey models.

This research investigates the intricate interplay among the digital economy, green innovation, and the level of sustainable development. Panel data from 268 cities in China, from 2011 to 2020, are used to comprehensively evaluate the level of digital economy development and investigate the digital economy’s influence on sustainable development. Additionally, a mechanism analysis is used to investigate the contribution of green innovation. The findings suggest that the digital economy significantly stimulates sustainable development, and green innovation serves as a mediating intermediary and moderating effect in facilitating this relationship. Moreover, the robustness check extends the verification of the positive effect of the “Broadband China” policy on sustainable development, strengthening the reliability of the results. The contribution of this study provides management insights on how regions can promote sustainable development in the digital age.

The digital economy enhances economic efficiency and improves economic structure, driving economic growth through transformations in efficiency, momentum, and quality. It has become a new driving force for advancing common prosperity. This study uses SDM, SDID, and SPSTR models to explore the impact of digital economy on common prosperity, which constructs the index system to evaluate the common prosperity from process index and outcome index. According to the panel data of 76 cities in the Yellow River Basin from 2011 to 2021, and the findings are as follows: (1) The digital economy exhibits a development pattern characterized by high activity downstream and lower activity upstream, and the development trend is stable. The development pattern of common prosperity has changed from sporadic distribution to regional agglomeration, and the level of common prosperity in most cities has improved. (2) The digital economy has a significant positive spatial effect on common prosperity. And the findings are robust after introducing the “Big Data” exogenous policy impact, dynamic SDM model, and other methods. Moreover, spatial heterogeneity exists. The promotion effect in the upper and lower reaches is stronger, while the middle reaches are weakly affected by the digital economy. (3) The spatial spillover effect of the digital economy on common prosperity has a boundary, and the positive spillover reaches a maximum value at 600–650 km. (4) Nonlinear analysis confirms that the digital economy provides momentum for common prosperity industrial structure optimization that can effectively stimulate the “endogenous” growth mechanism, strengthen the marginal increasing effect of the digital economy driving common prosperity and enhance the effect of “making a bigger pie”. The digital economy makes effective use of digital resources and technologies, promotes the equalization of public services, exerts a positive impact on the realization of common prosperity, and consolidates the effect of “dividing a better cake”.

Transition risks caused by climate change are becoming an important issue in finance research. In this study, we first construct the transmission mechanism of “climate change–change in investor attention–financial stability” and analyze the impact of transition risks on Chinese financial market stability. Second, we construct a Climate Change Index (CCI). The CCI depicts changes in investors’ attention to the transition risks of climate change based on the Baidu Index. We also use the dynamic factor model (DFM) to construct a Financial Stress Index (FSI) that describes the Chinese financial market stability. The FSI can also effectively identify financial events within the sample interval. We then use the TVP-VAR model to empirically analyze the impact of the transition risks of climate change on Chinese financial market stability. We present the following results: in the short and medium terms, more financial market pressure will be caused by an increase in the CCI. In the long run, the impact of an increase in CCI on Chinese financial market pressure is uncertain. Finally, we present valuable countermeasures and suggestions from the different perspectives of investors, financial institutions, and regulators.

IntroductionIn the digital era, new digital infrastructures (NDIs) play a pivotal role in fostering economic growth and technological innovation. However, their ecological impact, particularly on carbon dioxide emissions, remains underexplored. Addressing this gap holds significant practical and theoretical value.MethodsUtilizing panel data from 283 Chinese cities spanning 2009 to 2020, this study employs a two-way fixed-effects model to empirically assess the influence of NDIs on urban carbon emissions (UCE). Additionally, a mediation effect model is used to examine the mechanisms of this influence.ResultsThe findings reveal that: (1) NDIs significantly mitigate UCE levels, a conclusion supported by robustness tests involving instrumental variables and the exogenous policy shocks of smart city pilot programs; (2) NDIs primarily impact UCE through two channels: the digital economy and green technology innovation; and (3) heterogeneity analysis indicates that NDIs predominantly curb carbon emissions in cities with lower administrative levels, while positively contributing to UCE intensity in higher administrative level cities. Notably, NDIs substantially reduce UCE in non-old industrial cities, with a negligible effect in old industrial cities.DiscussionThis research expands the understanding of the economic-environmental implications of NDIs, offering valuable insights for policymakers regarding NDIs’ environmental impacts. It also provides strategic guidance for urban low-carbon transitions in the big data era.

This paper investigates the robust stability and stabilization of networked evolutionary games (NEGs) with time delays. First, a mathematical model is presented to describe the dynamics of NEG with time-varying delays and disturbances. Second, an auxiliary system is constructed using the semi-tensor product of matrices and a dimension augmenting technique. Then, a verification condition of robust stability is derived. Third, in order to stabilize NEG to the Nash equilibrium, the robust stability problem is transformed into the robust stabilization problem. Moreover, an algorithm is proposed to design the stabilization controller. Finally, the validity of the results is verified by an example.

Climate change-induced risks, such as global warming, can affect the economic development of entities and, consequently, the stability of financial markets. Businesses are progressively making the transition to green in order to lessen the negative consequences of climate threats. This study examines the relationship between corporate risk-taking (CRISK) and financialization (FIN) in light of climate change. The impact of business risk-taking on financialization is experimentally investigated through the transmission chain of “CRISK - enterprise value – FIN” using a fixed-effects model. The study also analyzes the moderating effect of climate change on the direct and indirect channels of climate change by using “temperature” and “investors’ concern about climate,” respectively. In addition, the empirical results are tested for robustness using propensity score matching and an instrumental variable method. This study’s findings reveal the following key insights. First, CRISK significantly enhances FIN by improving firm value. Second, enterprises with high financing constraints and manufacturing enterprises are more likely to have a positive correlation between CRISK and FIN. Third, the relationship between CRISK and FIN is enhanced by the direct transmission channel of increasing climate risk, but the indirect transmission channel is not significant. This study proposes policy recommendations to address the effect of climate risk on CRISK and FIN. Among these suggestions are the prudent distribution of financial resources among enterprises according to their level of risk-taking and the reinforcement of regulatory authorities’ financial oversight of businesses with high financing constraints and the manufacturing sector. By implementing these policies, companies can better manage climate-related risks and contribute to financial stability.