Qualitative behavior and computation of multiple solutions of singular nonlinear boundary value problems. (English) Zbl 1151.34309

Ballard, Grey; Baxley, John

Involve 1, No. 1, 21-31 (2008).

Summary: We consider boundary value problems of the form \(y^{\prime\prime}=-f(t,y),y(0)=0,y(1)=0,\) motivated by examples where \(f(t,y) = \varphi (t)g(y)\) and \(g(y)\) behave like \(y-\lambda(\lambda>0)\) as \(y\rightarrow 0+\). We explore conditions under which such problems have multiple positive solutions, investigate qualitative behavior of these solutions, and discuss computational methods for approximating the solutions.

MSC:

34B16	Singular nonlinear boundary value problems for ordinary differential equations
65L10	Numerical solution of boundary value problems involving ordinary differential equations

Keywords:

singular nonlinear boundary value problems; multiple solutions; shooting; computation; qualitative behavior