Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1186.34014
Rachuunková, Irena; Tomeček, Jan
Strictly increasing solutions of a nonlinear singular differential equation arising in hydrodynamics. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 3-4, A, 2114-2118 (2010). ISSN 0362-546X

Summary: This paper investigates singular initial problems $$(p(t)u')'=p(t)f(u),\quad u(0)=B,\ u'(0)=0,$$ on the half-line $[0,\infty)$. Here $B<0$ is a parameter, $p(0)=0$ and $p'(t)>0$ on $(0,\infty)$, $f(L)=0$ for some $L>0$ and $xf(x)<0$ if $L_0<x<L$ and $x\ne 0$. The existence of a strictly increasing solution to the problem for which there exists a finite $c>0$ such that $u(c)=L$ is discussed. This is fundamental for the existence of a strictly increasing solution of the problem having its limit equal to $L$ as $t\to\infty$, which has great importance in applications.

MSC 2000:: *34A12 Initial value problems for ODE
34C11 Qualitative theory of solutions of ODE: Growth, etc.

Keywords: singular ordinary differential equation of second order; time singularities; unbounded domain; strictly increasing solutions

Cited in: Zbl 1203.34058

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]