Abstract functional differential equations and reaction-diffusion systems

R. H. Martin, Hal Smith

Research output: Contribution to journalArticlepeer-review

562 Scopus citations


Several fundamental results on the existence and behavior of solutions to semilinear functional differential equations are developed in a Banach space setting. The ideas are applied to reaction-diffusion systems that have time delays in the nonlinear reaction terms. The techniques presented here include differential inequalities, invariant sets, and Lyapunov functions, and therefore they provide for a wide range of applicability. The results on inequalities and especially strict inequalities are new even in the context of semi linear equations whose nonlinear terms do not contain delays.

Original languageEnglish (US)
Pages (from-to)1-44
Number of pages44
JournalTransactions of the American Mathematical Society
Issue number1
StatePublished - Sep 1990


  • Differential inequalities
  • Invariant sets
  • Reaction-diffusion-delay systems
  • Semilinear functional differential equations

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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