期刊论文

Xu, Jiankai

英文

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS

1534-0392

2019

18

2

625-641

10.3934/cpaa.2019031

2000 Mathematics Subject Classification. Primary: 45E10; Secondary: 45G05. Key words and phrases. Bessel potential, integral equations, positive solutions, the regularity lifting theorem, integrability intervals, radial symmetry, decay rate. The first author is supported by the Scientific Research Fund of Hunan Provincial Education Department grant 16C0763 and 17C0754; The second author is supported by the NSF of China grant 11671086 and 11871208 and NSF of Hunan Province of China (No. 2018JJ2159); The third author is supported by the NSF of China grant 11771358. ∗ Corresponding author.

本校为通讯机构

This paper is devoted to exploring the properties of positive solutions for a class of nonlinear integral equation(s) involving the Bessel potentials, which are equivalent to certain partial differential equations under appropriate integrability conditions. With the help of regularity lifting theorem, we obtain an integrability interval of positive solutions and then extend the integrability interval to the whole [1;∞) by the properties of the Bessel kernels and some delicate analysis techniques. Meanwhile, the radial symmetry and the sharp ex...