Non-existence results for cooperative semi-linear fractional system via direct method of moving spheres

Abstract

In this article, we consider the cooperative semi-linear fractional system (−∆) α 2 u(x) = h(x, u(x)), where 0 < α < 2, u and h stand for k-dimentional vector-valued functions, and h(x, u(x)) is locally Lipschitz in u. We first establish two narrow region principles for different cases. Based on these principles, we use the direct method of moving spheres to prove the non-existence of positive solutions of the above system in bounded star-shaped domains and the whole space.

A Study of Data Governance Methods Based on Non-Linear Evaluation of K-Domains

“…First, in terms of data scale, the conventional data governance methods treat all data as two-dimensional data due to the lack of effective analysis of data dimensionality, which leads to some multidimensional data being severely compressed. On this basis, the completed data after processing loses its multidimensional characteristics, thus making the completed data differ greatly from the original data, and its data attributes are missing too much to replace the original data for processing [2]. In this regard, the data dimensions can be classified according to the different data attributes of the actual data as well as the data types, and according to the characteristics of the data attributes.…”