Annali di Matematica Pura ed Applicata

, Volume 165, Issue 1, pp 29–47 | Cite as

The boundedness and convergence of solutions of second-order differential equations with applications

  • Jiang Ji-Fa


For multidimensional second-order differential equations we present new conditions for the boundedness and convergence of all solutions and their derivatives, and the existence of periodic solutions. In particular, for scalar case we give the necessary and sufficient conditions for the boundedness and convergence of all solutions and their derivatives. These results are used to improve a result of Levin and Nohel for the reactor dynamics and a result of Holmes for the evolution equations derived from a conveying fluid and to give an answer to the conjecture on the continuous stirred tank proposed by Uppal etc.


Differential Equation Periodic Solution Evolution Equation Scalar Case Reactor Dynamic 
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© Fondazione Annali di Matematica Pura ed Applicata 1993

Authors and Affiliations

  • Jiang Ji-Fa
    • 1
  1. 1.Department of MathematicsAnhui Normal UniversityWuhu, AnhuiChina

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