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System of Fredholm Integral Equations: Existence Results via Brezis–Browder Arguments

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Constant-Sign Solutions of Systems of Integral Equations

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Abstract

In this chapter we shall consider the system of Fredholm integral equations

$$\displaystyle\begin{array}{rcl} & & u_{i}(t) = h_{i}(t) +\int _{ 0}^{T}g_{ i}(t,s)f_{i}(s,u_{1}(s),u_{2}(s),\cdots \,,u_{n}(s))ds, \\ & & \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad t \in [0,T],\ 1 \leq i \leq n {}\end{array}$$

where 0 < T < ∞, and also the following system on the half-line

$$\displaystyle\begin{array}{rcl} & & u_{i}(t) = h_{i}(t) +\int _{ 0}^{\infty }g_{ i}(t,s)f_{i}(s,u_{1}(s),u_{2}(s),\cdots \,,u_{n}(s))ds, \\ & & \qquad \qquad \qquad \qquad \qquad \qquad t \in [0,\infty ),\ 1 \leq i \leq n. {}\end{array}$$

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Authors and Affiliations

  1. Department of Mathematics, Texas A&M University – Kingsville, Kingsville, TX, USA

    Ravi P. Agarwal

  2. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Galway, Ireland

    Donal O’Regan

  3. School of Electrical & Electronic Engineering, Nanyang Technological University, Singapore, Singapore

    Patricia J. Y. Wong

Authors
  1. Ravi P. Agarwal
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  2. Donal O’Regan
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  3. Patricia J. Y. Wong
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Agarwal, R.P., O’Regan, D., Wong, P.J.Y. (2013). System of Fredholm Integral Equations: Existence Results via Brezis–Browder Arguments. In: Constant-Sign Solutions of Systems of Integral Equations. Springer, Cham. https://doi.org/10.1007/978-3-319-01255-1_19

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