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Integral Equations

In: Infinite Interval Problems for Differential, Difference and Integral Equations

Author

Listed:
  • Ravi P. Agarwal

    (National University of Singapore)

  • Donal O’Regan

    (University of Ireland)

Abstract

This chapter establishes existence theory of Fredholm and Volterra integral equations on infinite intervals. In Section 4.2 we consider the Fredholm integral equation (4.1.1) % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaiaacI % cacaWG0bGaaiykaiabg2da9iaadIgacaGGOaGaamiDaiaacMcacqGH % RaWkdaWdXaqaaiaadUgacaGGOaGaamiDaiaacYcacaWGZbGaaiykai % aadEgacaGGOaGaam4CaiaacYcacaWG4bGaaiikaiaadohacaGGPaGa % aiykaiaadsgacaWGZbGaaiilaiaabccacaqGGaacbiGaa8xyaiaa-5 % cacaWFLbGaaeiiaiaabccacaWG0bGaeyicI4Saai4waiaaicdacaGG % SaGaamivaiaacMcaaSqaaiaaicdaaeaacaWGubaaniabgUIiYdaaaa!5C2F! $$ x(t) = h(t) + \int_0^T {k(t,s)g(s,x(s))ds,{\text{ }}a.e{\text{ }}t \in [0,T)}$$ and the Volterra integral equation (4.1.2) % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaiaacI % cacaWG0bGaaiykaiabg2da9iaadIgacaGGOaGaamiDaiaacMcacqGH % RaWkdaWdXaqaaiaadUgacaGGOaGaamiDaiaacYcacaWGZbGaaiykai % aadEgacaGGOaGaam4CaiaacYcacaWG4bGaaiikaiaadohacaGGPaGa % aiykaiaadsgacaWGZbGaaiilaiaabccacaqGGaacbaGaa8xyaiaa-5 % cacaWFLbGaaeiiaiaabccacaWG0bGaeyicI4Saai4waiaaicdacaGG % SaGaamivaiaacMcaaSqaaiaaicdaaeaacaWG0baaniabgUIiYdaaaa!5C4D! $$ x(t) = h(t) + \int_0^t {k(t,s)g(s,x(s))ds,{\text{ }}a.e{\text{ }}t \in [0,T)}$$ both of which are defined on the half open interval [0,T) with 0 ≤ T ≤ ∞, and provide conditions under which these equations have solutions in L p [0,T), 1

Suggested Citation

  • Ravi P. Agarwal & Donal O’Regan, 2001. "Integral Equations," Springer Books, in: Infinite Interval Problems for Differential, Difference and Integral Equations, chapter 0, pages 139-232, Springer.
    • Handle: RePEc:spr:sprchp:978-94-010-0718-4_4
    DOI: 10.1007/978-94-010-0718-4_4
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