On some nonlinear ordinary differential equations with advanced arguments

✍ Scribed by Antoni Augustynowicz; Henryk Leszczyński; Wolfgang Walter

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 137 KB
• Volume: 53
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(02)00314-0

✦ Synopsis

The paper deals with ODEs with an advanced argument, in particular, with such equations as y (t) = (y(ÿt)) 1=ÿ , the simplest example is y (t) = y(2t). The corresponding initial-value problem with y(0) = y0 ¿ 0 has three types of solutions: (a) a unique analytic solution, (b) solutions of subexponential growth, and (c) for every ¿ 0 a solution that behaves like e t as t → ∞. In the case y0 = 0 there is (besides y ≡ 0) a positive solution, for some ÿ ¿ 1 it can be analytic, but the above example ÿ = 2 admits inÿnitely many analytic solutions.