With the rapid development of the global digital knowledge economy, educational activities are facing more challenges. Sustainable development education aims to cultivate students’ thinking ability to better integrate with the contemporary world view, so classroom practice should involve innovative teaching and learning. The goal of sustainable development education is to cultivate talents with high-level thinking and sustainable development abilities. The concept of deep learning emphasizes mobilizing students’ internal motivation, focusing on problem-solving ability, improving students’ critical thinking level, and developing students’ lifelong learning ability. The concept of deep learning has evolved with the times. The introduction of the concept of deep learning in teaching can enhance students’ understanding of the nature of knowledge, cultivate students’ high-level thinking, and enable students to achieve better learning results. Integrating the concept of deep learning into teaching has extremely important significance and value for sustainable development education. It has become a hot topic in the world to comprehensively analyze the research status of deep learning and explore how deep learning can help education achieve sustainable development. In this study, CiteSpace (6.1.R2) visualization analysis software was used to visualize and quantitatively analyze the literature on deep learning in the Social Science Citation Index (SSCI). The visualized analysis is conducted on the annual publication amount, authors, institutions, countries, keywords, and high-frequency cited words of deep learning, to obtain the basic information, development status, hot spots, and evolution trends of deep learning research. The results show that the annual publication volume of deep learning is on the rise; deep learning research has entered a rapid growth stage since 2007; the United States has published the most papers and is the center of the global deep learning research collaboration network; the countries involved in the study were often interconnected, but the institutions and authors were relatively dispersed; research in the field of deep learning mainly focuses on concept exploration, influencing factors, implementation strategies and effectiveness of deep learning; learning method, learning strategy, curriculum design, interactive learning environment are the high-frequency keywords of deep learning research. It can be seen that deep learning research has the characteristics of transnationality, multidisciplinary nature and multi-perspective. In addition, this paper systematically analyzes the latest progress in global deep learning research and objectively predicts that using intelligent technology to design appropriate teaching and learning scenarios and evaluation methods may become the future development trend of deep learning. The research results of this paper will help readers to have a comprehensive understanding of deep learning research, provide deeper and more targeted resources for integrating deep learning concepts into teaching, and promote better sustainable development of education.

In the paper, we study the existence of ground states for a nonlinear Schrödinger-Bopp-Podolsky system with asymptotically periodic potentials. As a consequence, we also prove ground states for the nonlinear Schrödinger-Bopp-Podolsky system with periodic potentials.

Self-regulated learning (SRL) has been an important topic in the field of global educational psychology research since the last century, and its emergence is related to researchers’ reflections on several educational reforms. To better study the research history and developmental trend of SRL, in this work, the Web of Science core collection database was used as a sample source, “self-regulated learning” was searched as the theme, and 1218 SSCI documents were collected from 30 September 1986, to 2022. We used CiteSpace software to visualize and analyze the number of publications, countries, institutions, researchers, keywords, highly cited literature, authors’ co-citations, keyword clustering, and timeline in the field of self-regulated learning research, and to draw related maps. It was found that the articles related to self-regulated learning were first published in the American Journal of Educational Research in 1986, and that self-regulated learning-related research has received increasing attention in recent decades, wherein research on self-regulated learning is roughly divided into three periods: the budding period from 1986 to 2002, the flat development period from 2003 to 2009, and the rapid development period from 2010 to 2022. The number of papers published in the United States, China, Australia, and Germany is relatively high, and the number of papers published in Spain is low compared with that in the United States. During this period, the University of North Carolina in the United States and McGill University in Canada were the institutions with the most publications; Azevedo Roger and Lajoie Susanne P were the most-published scholars in the field of self-regulated learning research; the journal publication with the highest impact factor was Computers Education; and the primary research interests in self-regulated learning mainly focused on Performance, Strategy, Students, Achievement, Motivation, and Metacognition. Furthermore, the most-cited study related to SRL research was Formative assessment and self-regulated learning: a model and seven principles of good feedback practice.

In the paper, by using the variational methods we study a non-autonomous Schrödinger-Bopp-Podolsky system, where a > 0, 3 < p < 4 are fixed, λ > 0 is a parameter, and the potentials V, Q satisfy appropriate assumptions. We give some existence results, depending on the parameter λ. Moreover the results are still valid for the classical Schrödinger-Poisson system.

In this paper, we study a class of Kirchhoff type problems with resonance \begin{equation*} \begin{cases} -\left(a+b\displaystyle\int_{\Omega}|\nabla u|^2dx\right)\Delta u=\nu u^{3}+ \lambda |u|^{q-1}u,&\rm \mathrm{in}\ \ \Omega, \\ u=0, &\rm \mathrm{on} \ \ \partial\Omega, \end{cases} \end{equation*} where $\Omega\subset \mathbb{R}^{3}$ is a bounded domain, $a,b,\nu,\lambda>0$ and $0< q <1$. By a minimizing method, we obtain the existence of positive ground state solutions for all $0<\nu\leq b\nu_{1}$ and $\lambda>0$. Furthermore, using the Nehari method, we obtain two positive solutions for all $\nu>b\nu_{1}$ and $0<\lambda<\tilde{\lambda},$ where $\nu_{1}$ is the first eigenvalue of problem (5) and $\tilde{\lambda}$ is a positive constant. And one of the two positive solutions is a ground state solution.

We study the following singular elliptic equation with critical exponent $$ \begin{cases} -\varDelta u=Q(x)u^{2^{*}-1}+\lambda u^{-\gamma}&\text{in } \varOmega, \\ u \gt 0 &\text{in } \varOmega, \\ u=0 &\text{on } \partial\varOmega, \end{cases} $$ where $