Monge-Ampere equations have important research significance in many fields such as geometry, convex geometry and mathematical physics. In this paper, under some superlinear and sublinear conditions, the existence of nontrivial solutions for a system arising from Monge-Ampere equations with two parameters is investigated based on Guo-Krasnosel'skii fixed point theorem. In the end, two examples are given to illustrate our main results.

Integrated cultivation strategies can significantly improve rice yield. However, it is unclear how integrated cultivation practices improve soil microbial diversity and its related mechanism in rice field. Therefore, four integrated cultivation practices i.e., no N application (N0), local farmers’ practice (FP), high-yield and high-efficiency practice (HYEY), and super-high-yield cultivation practice, impacts on soil properties and structure composition of microbial community were explored. Compared with N0, SHY treatment, significantly increased soil alkaline nitrogen and organic matter contents. HYHE and SHY treatments significantly altered soil fungal community and Alpha diversity. Based on Venn diagram analysis, the composition of bacterial communities under all treatments was similar, but with different compositions of fungal communities. Cluster analysis indicates that the Proteobacteria was the absolute dominant group of bacterial communities, and Chloroflexi, Bacteroidetes, and Acidobacteria were the dominant group. Different cultivation methods also led to changes in the main factors affecting soil bacteria and fungi composition. Available potassium and organic matter were the main environmental factors that affected bacteria, with the strong of available potassium on the soil. To sum up, SHY and HYEY were beneficial management options in terms of improved soil fertility Alpha diversity of the soil bacterial community respectively.

Habitat quality has great significance for regional ecological conservation and human welfare. In this study, we evaluated the spatial and temporal characteristics of land use and habitat quality in the temperate desert sub-region of Ordos Plateau using patch-generating land use simulation (PLUS) and integrated valuation of ecosystem services and trade-offs (InVEST) models. From 2000 to 2020, the areas of grassland, cropland, and unused land in the study area increased significantly; the areas of water bodies and woodland increased slightly; and the area of wasteland decreased significantly. Moreover, the habitat quality in the temperate desert subzone of the Ordos Plateau showed a trend of increasing and then decreasing from 2000 to 2020. The areas of lower and low habitat quality first decreased and then increased, and the overall area decreased over time. Conversely, the areas of high and higher habitat quality initially increased and then decreased, and the overall area increased over time. The area of medium habitat quality first decreased and then increased, although the overall change was minimal. Based on the PLUS model, the habitat quality of the study area in 2025 predicted under the natural development scenario was compared with that predicted under the ecological conservation scenario, showing higher habitat quality and lower habitat degradation under the ecological conservation development scenario. These results can be used to provide a scientific basis and decision reference for the sustainable use of land resources and high-quality socio-economic development in the temperate desert sub-region of the Ordos Plateau.