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Positive solutions of a singular nonlinear third order two-point boundary value problem. (English) Zbl 1111.34022
Summary: Some existence results on positive solutions for the following singular nonlinear third-order two-point boundary value problem \[ x'''(t)-\alpha(t) f(t,x(t))=0,\quad a<t<b,\qquad x(a)=x(b)=x''(b)=0, \] are established, where \(\alpha\in C((a,b),[0,+\infty))\) \(f\in C([a,b]\times (0,+\infty))\), \([0,+\infty))\), \(\alpha(t)\) may be singular at \(t=a,b\) and \(f(t,x)\) may be singular at \(x=0\).

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