## 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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