EXISTENCE OF HOMOCLINIC ORBITS FOR LI¶ENARD TYPE SYSTEMS

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2010, v.17 no.4, pp.389-396

Kim, Yong-In (Department of Mathematics, University of Ulsan)

Kim, Yong-In. (2010). EXISTENCE OF HOMOCLINIC ORBITS FOR LIENARD TYPE SYSTEMS. 한국수학교육학회지시리즈B:순수및응용수학, 17(4), 389-396.

복사

Abstract

We investigate the existence of homoclinic orbits of the following systems of <TEX>$Li{\'{e}}nard$</TEX> type: <TEX>$a(x)x^'=h(y)-F(x)$</TEX>, <TEX>$y^'$</TEX>=-a(x)g(x), where <TEX>$h(y)=m{\mid}y{\mid}^{p-2}y$</TEX> with m > 0 and p > 1 and a, F, 9 are continuous functions such that a(x) > 0 for all <TEX>$x{\in}{\mathbb{R}}$</TEX> and F(0)=g(0)=0 and xg(x) > 0 for <TEX>$x{\neq}0$</TEX>. By a series of time and coordinates transformations of the above system, we obtain sufficient conditions for the positive orbits of the above system starting at the points on the curve h(y) = F(x) with x > 0 to approach the origin through only the first quadrant. The method of this paper is new and the results of this paper cover some early results on this topic.

keywords: Lienard type system, homoclinic orbit, phase plane analysis

참고문헌

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논문 상세

Vol.17 No.4

EXISTENCE OF HOMOCLINIC ORBITS FOR LIENARD TYPE SYSTEMS

EXISTENCE OF HOMOCLINIC ORBITS FOR LI¶ENARD TYPE SYSTEMS

Abstract

참고문헌

한국수학교육학회지시리즈B:순수및응용수학