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Nontrivial Solutions for Asymptotically Positive Linear Duffing Equations(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2012年02期
Page:
29-31
Research Field:
数学
Publishing date:

Info

Title:
Nontrivial Solutions for Asymptotically Positive Linear Duffing Equations
Author(s):
Wang Weiqin1; 2
1.Dept of Math,Taizhou Teachers College,Taizhou,225300,China
Keywords:
asymptotically positive linear Duffing equations; existence of nontrivial solutions; classification theory of positively linear Duffing equations; Fuˇck spectrum; homotopy continutation method
PACS:
O175
DOI:
-
Abstract:
In this paper we mainly study the nontrivial solutions for asymptotically positive linear Duffing equations: x″ + f( t，x) = 0， x( 0) cosα － x’( 0) sinα = 0， x( 1) cosβ － x’( 1) sinβ = 0． We first introduce the classification theory of homogenous Sturm － Liouville boundary value problem for positively linear Duffing equations: ( p( t) x’( t) ) ’ + q + ( t) x + － q － ( t) x － = 0， x( 0) cosα － p( 0) x’( 0) sinα = 0， x( 1) cosβ － p( 1) x’( 1) sinβ = 0 and then investigate the existence of nontrivial solutions of asymptotically positive linear Duffing equations． The main methods in the discussion are the classification theory of linear homogenous equations and some results of the Leray- Schauder degree．

References:

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Last Update: 2013-03-11