Stability and monotonicity properties of stiff quasilinear boundary problems. (English) Zbl 0546.34046

Lorenz, Jens

Zb. Rad., Prir.-Mat. Fak., Univ. Novom Sadu, Ser. Mat. 12, 151-175 (1982).

The author studies the nonlinear two-point boundary value problem of singular perturbation type \(-eu''+a(x,u)u'+b(x,u)=0,\) 0\(\leq x\leq 1\), \(u(0)=A\), \(u(1)=B\) where e is a small parameter. He makes no assumptions about the behavior of the \(e=0\) problem. The paper gives sufficient conditions for existence, uniqueness, and stability of solutions of the boundary value problem.

Reviewer: A.Hausrath

MSC:

34D20	Stability of solutions to ordinary differential equations
34B15	Nonlinear boundary value problems for ordinary differential equations
34B10	Nonlocal and multipoint boundary value problems for ordinary differential equations
65L10	Numerical solution of boundary value problems involving ordinary differential equations

Keywords:

nonlinear two-point boundary value problem; singular perturbation; small parameter; existence; uniqueness; stability