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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 $$x=0$$.

##### MSC:
 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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