Positive periodic solutions of functional differential equations
نویسنده
چکیده
We consider the existence, multiplicity and nonexistence of positive o-periodic solutions for the periodic equation x0ðtÞ 1⁄4 aðtÞgðxÞxðtÞ lbðtÞf ðxðt tðtÞÞÞ; where a; bACðR; 1⁄20;NÞÞ are o-periodic, Ro 0 aðtÞ dt40; Ro 0 bðtÞ dt40; f ; gACð1⁄20;NÞ; 1⁄20;NÞÞ; and f ðuÞ40 for u40; gðxÞ is bounded, tðtÞ is a continuous o-periodic function. Define f0 1⁄4 limu-0þ f ðuÞ u ; fN 1⁄4 limu-N f ðuÞ u ; i0 1⁄4 number of zeros in the set f f0; fNg and iN 1⁄4 number of infinities in the set f f0; fNg: We show that the equation has i0 or iN positive o-periodic solution(s) for sufficiently large or small l40; respectively. r 2004 Elsevier Inc. All rights reserved.
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تاریخ انتشار 2004