Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Oscillation and Nonoscillation of Nonlinear Neutral Delay Differential Equations with Several Positive and Negative Coefficients

  • Elabbasy, Elmetwally M. (Department of Mathematics, Faculty of Science, Mansoura University) ;
  • Hassan, Taher S. (Department of Mathematics, Faculty of Science, Mansoura University) ;
  • Saker, Samir H. (Department of Mathematics, Faculty of Science, Mansoura University)
  • Received : 2005.09.16
  • Published : 2007.03.23
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Abstract

In this paper, oscillation and nonoscillation criteria are established for nonlinear neutral delay differential equations with several positive and negative coefficients $$[x(t)-R(t)x(t-r)]^{\prime}+\sum_{i=1}^{m}Pi(t)H_i(x(t-{\tau}_i))-\sum_{j=1}^{n}Q_j(t)H_j(x(t-{\sigma}_j))=0$$. Our criteria improve and extend many results known in the literature. In addition we prove that under appropriate hypotheses, if every solution of the associated linear equation with constant coefficients, $$y^{\prime}(t)+\sum_{i=1}^{m}(p_i-\sum_{k{\in}J_i}qk)y(t-{\tau}_i)=0$$, oscillates, then every solution of the nonlinear equation also oscillates.

Keywords

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