On Positive solutions of integral equations with the weighted Bessel potentials

Mingchun Wang; Jiankai Xu; Huoxiong Wu

doi:10.3934/cpaa.2019031

Article Contents

2019, Volume 18, Issue 2: 625-641. Doi: 10.3934/cpaa.2019031

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On Positive solutions of integral equations with the weighted Bessel potentials

1.
College of mathematical econometric, Hunan university, Hunan, Changsha, 410082, China
2.
College of Sciences, Hunan Agriculture University, Hunan, Changsha, 410128, China
3.
School of Mathematical Sciences, Xiamen University, Fujian, Xiamen 361005, China

* Corresponding author
* Corresponding author

Received: December 2017

Revised: June 2018

Published: October 2018

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

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Abstract

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 exponential decay of positive solutions are also obtained. Furthermore, as an application, we establish the uniqueness theorem of the corresponding partial differential equations.

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Mathematics Subject Classification: Primary: 45E10; Secondary: 45G05.

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