Equations on Time Scales

Ravi P. Agarwal and Donal O’Regan
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Ravi P. Agarwal: National University of Singapore
Donal O’Regan: University of Ireland

Chapter Chapter 8 in Infinite Interval Problems for Differential, Difference and Integral Equations, 2001, pp 329-338 from Springer

Abstract: Abstract In this chapter existence results are presented for time scale boundary value problems on infinite intervals. Our results are based on a growth argument as well as on a upper and lower solution idea. We recall that a time scale T is an arbitrary nonempty closed subset of the real numbers ℝ. The forward (respectively, backward) jump operator at t for t inf T) is defined by % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4WdmNaai % ikaiaadshacaGGPaGaeyypa0JaciyAaiaac6gacaGGMbWaaiWaaeaa % cqaHepaDcqGH+aGpcaWG0bGaaiOoaiabes8a0jabgIGioJqaaiaa-r % faaiaawUhacaGL9baacaqGGaGaaeiiamaabmaabaGaaeOCaiaabwga % caqGZbGaaeiCaiaabwgacaqGJbGaaeiDaiaabMgacaqG2bGaaeyzai % aabYgacaqG5bGaaeilaiaabccacaqGGaGaeqyWdiNaaiikaiaadsha % caGGPaGaeyypa0Jaci4CaiaacwhacaGGWbWaaiWaaeaacqaHepaDcq % GH8aapcaWG0bGaaiOoaiabes8a0jabgIGiolaa-rfaaiaawUhacaGL % 9baaaiaawIcacaGLPaaaaaa!6B83! $$ \sigma (t) = \inf \left\{ {\tau > t:\tau \in T} \right\}{\text{ }}\left( {{\text{respectively, }}\rho (t) = \sup \left\{ {\tau

Date: 2001
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DOI: 10.1007/978-94-010-0718-4_8

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