First Order Integrodifferential Equations

Ravi P. Agarwal, Donal O’Regan and Patricia J. Y. Wong
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Ravi P. Agarwal: National University of Singapore, Department of Mathematics
Donal O’Regan: National University of Ireland, Department of Mathematics
Patricia J. Y. Wong: Nanyang Technological University, Division of Mathematics

Chapter Chapter 24 in Positive Solutions of Differential, Difference and Integral Equations, 1999, pp 386-394 from Springer

Abstract: Abstract In this chapter we shall present a result which establishes the existence of nonnegative solutions of the periodic boundary value problem involving the first order integrodifferential equation, namely, 24.1 $$\begin{array}{*{20}{c}} {y'(t) = Fy(t) a.e. on [0,T]} \\ {y(0) = y(T)} \\ \end{array}$$ where y ∈ C[0,T] and F is given by 24.2 $$Fy(t) = r(t) + y(t)g(t,y(t)) + h(t,y(t)) + \int_0^t {{k_1}(t,s){f_1}(s,y(s))ds + \int_0^T {{k_2}(t,s){f_2}(s,y(s))dsa.e.on[0,T];} } $$ here r : [0,T] → ℝ, g, h, f 1, f 2 : [0,T] × ℝ → ℝ, k 1 : [0,T] × [0,t] → ℝ and k 2 : [0,T] × [0,T] → ℝ.

Date: 1999
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DOI: 10.1007/978-94-015-9171-3_24

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