L^P solutions to the parameterized Fredholm integral equations associated with Chandrasekhar kernels

ABSTRACT

In this article, we study the $L^p$ solution of the Fredholm integral equation with parameters. On the one hand, we use Hilbert-type inequality to study Chandrasekhar-type integral operators, generalize the reachability results for the norm of the Chandrasekhar integral operator, and establish the existence and uniqueness results of the solutions of Chandrasekhar-type integral equations with parameters. On the other hand, we develop an iterative kernel technique for integral equations in infinite intervals, and construct series solutions of general Fredholm integral equations with parameters in different $L^p$ spaces.

Keywords:

• Chandrasekhar kernel
• Hilbert-type inequality
• Fredholm integral equation
• fixed-point theorem
• $L^p$ solution

2010 Mathematics Subject Classifications:

• Primary: 45B05
• Secondary: 26D15
• 47H10

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

Sheng-Ya Feng is partially supported by the National Natural Science Foundation of China [grant number 11501203, 11426109], the China Postdoctoral Science Foundation [grant number 2016M600278], and the National Foundation of China Scholarship Council [grant number 201806745028). Der-Chen Chang is partially supported by an National Science Foundation (NSF) [grant number DMS-1408839] and a McDevitt Endowment Fund at Georgetown University.