Non-monotone positive solutions of second-order linear differential equations: Existence, nonexistence and criteria

Mervan Pašić, Satoshi Tanaka

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

We study non-monotone positive solutions of the second-order linear differential equations: (p(t)x′)′ + q(t)x = e(t), with positive p(t) and q(t). For the first time, some criteria as well as the existence and nonexistence of non-monotone positive solutions are proved in the framework of some properties of solutions θ(t) of the corresponding integrable linear equation: (p(t)θ′)′ = e(t). The main results are illustrated by many examples dealing with equations which allow exact non-monotone positive solutions not necessarily periodic. Finally, we pose some open questions.

Original languageEnglish
JournalElectronic Journal of Qualitative Theory of Differential Equations
Volume2016
DOIs
Publication statusPublished - 2016

Keywords

  • Criteria
  • Existence
  • Non-monotonic behaviour
  • Nonexistence
  • Positive solutions

ASJC Scopus subject areas

  • Applied Mathematics

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