Global uniqueness of homoclinic orbits for a class of fourth order equations

C. J. Amick; J. F. Toland

doi:10.1007/BF00946252

Global uniqueness of homoclinic orbits for a class of fourth order equations

C. J. Amick, J. F. Toland

Department of Mathematical Sciences

University of Chicago

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we show the global existence and uniqueness of certain orbits homoclinic to the zero stationary solution of the fourth order equation {Mathematical expression} when α, γ>0>β, dk/dx<0 for x>0 and K(0)=0. The existence problem is approached via the general theory of [1] and uniqueness follows from the Maximum Principle and some geometrical observations about the role of convexity. There are no small amplitude assumptions.

Original language	English
Pages (from-to)	591-597
Number of pages	7
Journal	ZAMP Zeitschrift für angewandte Mathematik und Physik
Volume	43
Issue number	4
DOIs	https://doi.org/10.1007/BF00946252
Publication status	Published - 1 Jul 1992

ASJC Scopus subject areas

General Mathematics
General Physics and Astronomy
Applied Mathematics

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10.1007/BF00946252

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title = "Global uniqueness of homoclinic orbits for a class of fourth order equations",

abstract = "In this paper we show the global existence and uniqueness of certain orbits homoclinic to the zero stationary solution of the fourth order equation \{Mathematical expression\} when α, γ>0>β, dk/dx<0 for x>0 and K(0)=0. The existence problem is approached via the general theory of [1] and uniqueness follows from the Maximum Principle and some geometrical observations about the role of convexity. There are no small amplitude assumptions.",

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AU - Toland, J. F.

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N2 - In this paper we show the global existence and uniqueness of certain orbits homoclinic to the zero stationary solution of the fourth order equation {Mathematical expression} when α, γ>0>β, dk/dx<0 for x>0 and K(0)=0. The existence problem is approached via the general theory of [1] and uniqueness follows from the Maximum Principle and some geometrical observations about the role of convexity. There are no small amplitude assumptions.

AB - In this paper we show the global existence and uniqueness of certain orbits homoclinic to the zero stationary solution of the fourth order equation {Mathematical expression} when α, γ>0>β, dk/dx<0 for x>0 and K(0)=0. The existence problem is approached via the general theory of [1] and uniqueness follows from the Maximum Principle and some geometrical observations about the role of convexity. There are no small amplitude assumptions.

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ER -

Global uniqueness of homoclinic orbits for a class of fourth order equations

Abstract

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