System of Fredholm Integral Equations: Semipositone and Singular Case

Ravi P. Agarwal, Donal O’Regan and Patricia J. Y. Wong
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Ravi P. Agarwal: Texas A&M University – Kingsville, Department of Mathematics
Donal O’Regan: National University of Ireland, Galway, School of Mathematics, Statistics and Applied Mathematics
Patricia J. Y. Wong: Nanyang Technological University, School of Electrical & Electronic Engineering

Chapter Chapter 6 in Constant-Sign Solutions of Systems of Integral Equations, 2013, pp 175-207 from Springer

Abstract: Abstract In this chapter we shall consider two systems of integral equations, one is on a finite interval 6.1.1 $$\displaystyle{ u_{i}(t) = \mu \int _{0}^{1}g_{ i}(t,s)f(s,u_{1}(s),u_{2}(s),\cdots \,,u_{n}(s))ds,\ \ t \in [0,1],\ 1 \leq i \leq n }$$ and the other is on the half-line [0,∞) 6.1.2 $$\displaystyle{ u_{i}(t) = \mu \int _{0}^{\infty }g_{ i}(t,s)f(s,u_{1}(s),u_{2}(s),\cdots \,,u_{n}(s))ds,\ \ t \in [0,\infty ),\ 1 \leq i \leq n. }$$ In both (6.1.1) and (6.1.2), μ is a positive number, the function f may take negative values, and $$f(\cdot,u_{1},u_{2},\cdots \,,u_{n})$$ may be singular at u j = 0, $$j \in \{ 1,2,\cdots \,,n\}.$$

Keywords: Semipositone; Singular Integral Equations; Negative Values; Constant Sign Solutions; Chemical Reactor Theory (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-3-319-01255-1_6

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