A class of fourth order singular boundary value problems. (English) Zbl 1057.34006

Wei, Zhongli

Appl. Math. Comput. 153, No. 3, 865-884 (2004).

The author deals with the singular boundary value problem for the fourth-order ordinary differential equation \[ \begin{gathered} x^{(4)}(t)= f(t,x(t),-x''(t)), \qquad t\in (0,1),\\ x(0)= x(1)= 0, \quad ax''(0)- bx'''(0)= 0, \quad cx''(1)+ dx'''(1)= 0. \end{gathered} \tag{1} \] The author presents a sufficient and necessary condition for the existence of \(C^2([0,1])\) as well as \(C^3([0,1])\) positive solutions for (1) by constructing lower and upper solutions.

Reviewer: Messoud A. Efendiev (Berlin)

MSC:

34B16	Singular nonlinear boundary value problems for ordinary differential equations
34B18	Positive solutions to nonlinear boundary value problems for ordinary differential equations

Keywords:

singular boundary value problem; positive solution; lower and upper solution; maximum principle

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