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SOLVABILITY OF A THIRD ORDER NONLINEAR NEUTRAL DELAY DIFFERENTIAL EQUATION

  • Liu, Zeqing (Department of Mathematics Liaoning Normal University) ;
  • Wang, Wei (Department of Mathematics Liaoning Normal University) ;
  • Park, Jong Seo (Department of Mathematics Education Chinju National University of Education) ;
  • Kang, Shin Min (Department of Mathematics and RINS Gyeongsang National University)
  • Received : 2010.03.18
  • Accepted : 2010.06.01
  • Published : 2010.09.30

Abstract

This work deals with the existence of uncountably many bounded positive solutions for the third order nonlinear neutral delay differential equation $$\frac{d^3}{dt^3}[x(t)+p(t)x(t-{\tau})]+f(t,x(t-{{\tau}_1}),{\ldots},x(t-{{\tau}_k}))=0,\;t{\geq}t_0$$ where ${\tau}>0$, ${\tau}_i{\in}{\mathbb{R}^+}$ for $i{\in}\{1,2,{\ldots},k\}$, $p{\in}C([t_0,+{\infty}),{\mathbb{R}^+})$ and $f{\in}C([t_0,+{\infty}){\times}{\mathbb{R}^k},{\mathbb{R}})$.

Keywords

Acknowledgement

Supported by : Natural Science Foundation of Liaoning Province

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