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17 May 2004 Subdominant positive solutions of the discrete equation $\Delta u(k+n)=-p(k)u(k)$
Jaromír Baštinec, Josef Diblík
Abstr. Appl. Anal. 2004(6): 461-470 (17 May 2004). DOI: 10.1155/S1085337504306056


A delayed discrete equation Δu(k+n)=p(k)u(k) with positive coefficient p is considered. Sufficient conditions with respect to p are formulated in order to guarantee the existence of positive solutions if k. As a tool of the proof of corresponding result, the method described in the author's previous papers is used. Except for the fact of the existence of positive solutions, their upper estimation is given. The analysis shows that every positive solution of the indicated family of positive solutions tends to zero (if k) with the speed not smaller than the speed characterized by the function k·(n/(n+1))k. A comparison with the known results is given and some open questions are discussed.


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Jaromír Baštinec. Josef Diblík. "Subdominant positive solutions of the discrete equation $\Delta u(k+n)=-p(k)u(k)$." Abstr. Appl. Anal. 2004 (6) 461 - 470, 17 May 2004.


Published: 17 May 2004
First available in Project Euclid: 1 June 2004

zbMATH: 1078.39004
MathSciNet: MR2063054
Digital Object Identifier: 10.1155/S1085337504306056

Primary: 39A10 , 39A11

Rights: Copyright © 2004 Hindawi

Vol.2004 • No. 6 • 17 May 2004
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