Classification of initial data for the Riccati equation

N. Chernyavskaya, L. Shuster

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We consider a Cauchy problem y′(x)+y2(x)=q(x), y(x)\x= x0=y0 where x0,y0∈R e q(x) ∈ L1loc(R) is a non-negative function satisfying the condition: ∫x -∞ q(t) dt > 0, ∫x q(t) dt > 0 for x ∈ R. We obtain the conditions under which y(x) can be continued to all of R. This depends on x0, y0 and the properties of q(x).

Original languageEnglish
Pages (from-to)511-525
Number of pages15
JournalBollettino della Unione Matematica Italiana B
Volume5
Issue number2
StatePublished - 1 Jun 2002

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