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Second order nonlinear differential equations Existence


6-05-13 * potato wide. Western Teachers College (Natural Science Edition 】 Volume 13 (Ⅳ) there is a continuous function ( ) + m a d a woman . . t here is a big positive. Under these conditions , we have the assumption of Theorem l (I) ~ (N) holds, then the system C2) existence of periodic solutions of period m . Proof (£),[link widoczny dla zalogowanych],( f) is ( 3) any Qiang , we should permit (£), j, (f) is bounded . For any 1 > 0, in the region 0 ≤ f ≤ T, + y ≥ Velvet , consider the function of a W0. ,) a exp (~ /-G (t,) + c + H () a zII () Id I ( chu +£)£)( 5) by the conditions of IYI one. . When H (j,) one. . Easy to know that W (t,, j,) one. . , And W (t,,) on (3) base derivative w ix (f,,) a exp (, plant c million. { is not the (+ a ) ​​_flI - k - t} v from the condition f1) to know 7 <fl outside the l I - :: Blue ::=::< 2G (t,) + c + H (j,) by the 0 ≤ (j,) and 0 ≤ f (x, Y) Y know (6 ) Is a Wf3 】 (f,,) < A lexp (k / G (t,) + c + H (j,) e () I 0 as a (+))< Iyl one. . When u (£., j,) one. . However, this implies w ix To be Extended to the t-T, the arbitrary nature of the knowledge of 1 (3 ) of the solution are there for all £ . and then the D: 0 ≤ t <+。。, d <<6, Y ≥ to consider the function t, X.y) a exp (+ 『 = ix D2: 0 ≤ t <+。。, n <<b, Y ≤ k , consider a function of r...) a exp (x + Jd by ( ) A ∞, and DI in the region , and by the conditions (Ⅲ), (N) know that V (f,, j,) ≥ 0, and in the regional D, V (,, Y) ≤ 0, so the literature [I] Theorem I5.7 of the conditions are met, using Theorem will know the system f3) to equation ( 2 ) the existence of periodic solutions of period , end card . Acknowledgements This paper is in the Guangxi Normal Imperial College Department of Mathematics and Computer Science, even when the complete repair of Feng Chunhua grateful for the guidance of teachers