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

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
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