System of Fredholm Integral Equations: Existence of a Constant-Sign L p Solution

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 5 in Constant-Sign Solutions of Systems of Integral Equations, 2013, pp 147-174 from Springer

Abstract: Abstract In this chapter we shall consider two systems of integral equations, one is on a finite interval 5.1.1 $$\displaystyle{ u_{i}(t) =\int _{ 0}^{1}g_{ i}(t,s)f(s,u_{1}(s),u_{2}(s),\cdots \,,u_{n}(s))ds,\ \ t \in [0,1],\ 1 \leq i \leq n }$$ and the other is on the half-line [0, ∞) 5.1.2 $$\displaystyle{ u_{i}(t) =\int _{ 0}^{\infty }g_{ i}(t,s)f(s,u_{1}(s),u_{2}(s),\cdots \,,u_{n}(s))ds,\ \ t \in [0,\infty ),\ 1 \leq i \leq n. }$$ In both (5.1.1) and (5.1.2), we shall include both cases when the function f is “nonnegative” as well as when f may take “negative” values.

Keywords: Fredholm Integral Equation; Skii Fixed Point Theorem; Constant Sign Solutions; Positive Continuous Solution; Semipositone (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-3-319-01255-1_5

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