Quasilinear and quadratic singularly perturbed Neumann’s problem. (English) Zbl 0937.34023

Vrábel’, Róbert

Math. Bohem. 123, No. 4, 405-410 (1998).

Boundary conditions of the form \(y'(a,\varepsilon)=0, y'(b,\varepsilon)=0\) are considered along with singularly perturbed equations of the form \(\varepsilon y''=F(t,y,y')\) on \((a,b)\). Existence and asymptotic behaviour of solutions are studied in the case when \[ F(t,y,y')=f(t,y)y'+g(t,y)\quad \text{or}\quad F(t,y,y')=f(t,y)y'{}^2+g(t,y). \]

Reviewer: Š.Schwabik (Praha)

MSC:

34B20	Weyl theory and its generalizations for ordinary differential equations
34E15	Singular perturbations for ordinary differential equations

Keywords:

singular perturbation; Neumann problem