New existence and multiplicity of homoclinic solutions for second order non-autonomous systems

In this paper, we study the second order non-autonomous system \begin{eqnarray*} \ddot{u}(t)+A\dot{u}(t)-L(t)u(t)+\nabla W(t,u(t))=0, \ \ \forall t\in\mathbb{R}, \end{eqnarray*} where $A$ is an antisymmetric $N\times N$ constant matrix, $L\in C(\mathbb{R},\mathbb{R}^{N\times N})$ may not be uniformly positive definite for all $t\in\mathbb{R}$, and $W(t,u)$ is allowed to be sign-changing and local superquadratic. Under some simple assumptions on $A$, $L$ and $W$, we establish some existence criteria to guarantee that the above system has at least one homoclinic solution or infinitely many homoclinic solutions by using mountain pass theorem or fountain theorem, respectively. Recent results in the literature are generalized and significantly improved

Investigation and Research on the Demands of Parents of Infants Aged 0-3 for the Teaching Staff in Nursery Care Institutions —Taking District A of Qingdao City as an Example

In recent years, the national attention towards the construction of the teaching contingent for nursery care services has been escalating annually. Families with multiple children are in an acute exigency for high-caliber teaching staff in nursery care services. Nevertheless, the professional proficiency of the teaching staff engaged in infant nursery care services still cries out for enhancement. Hence, this research zeroes in on parents of infants aged 0-3 as the research subjects and deploys the questionnaire survey method and the interview approach to endeavor to dissect the current state of the parental requirements for the teaching staff in nursery care institutions.This research principally employs the questionnaire method to probe into the parental requisites for the teaching staff in nursery care institutions and the extant circumstances of the teaching staff in five nursery care institutions in Qingdao City, supplemented by interviews. The findings manifest that there exist both overall and individual variances in the parental demands for the teaching staff in nursery care institutions. With respect to the professional echelon of teachers in nursery care institutions, factors such as the length of service, educational attainment, institutional nature, and the monthly age of infants all exert a conspicuous influence on the professional caliber of teachers

Mechanism of Green Finance Awareness on Sustainable Competitiveness of SMEs

One phenomenon observed during environmental problems was increased green finance in most countries. This study explores the mechanisms of green finance, sustainable competitiveness, and supply chain among SMEs. Self-administered online questionnaires were completed by 738, 314, and 210 senior managers respectively from China, Malaysia, and Singapore. SPSS and Smart PLS-SEM software were used to test the hypotheses. This study aligns with Sustainable Development Goal 11, i.e., sustainable cities and communities, and Sustainable Development Goal 13, i.e., climate action. This study echoes the China government's "double-carbon" target initiative presented in the 75th session of the United Nations General Assembly. Keywords: Human Capital Index in Malaysia, Early Education, Economic growth, Future Productivity eISSN: 2398-4287 © 2023. The Authors. Published for AMER & cE-Bs by e-International Publishing House, Ltd., UK. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer–review under responsibility of AMER (Association of Malaysian Environment-Behaviour Researchers), and cE-Bs (Centre for Environment-Behaviour Studies), College of Built Environment, Universiti Teknologi MARA, Malaysia. DOI: https://doi.org/10.21834/ebpj.v8i24.463