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Positive solutions of nonlinear singular third-order two-point boundary value problem. (English) Zbl 1107.34019
Summary: We are concerned with the existence of single and multiple positive solutions to the nonlinear singular third-order two-point boundary value problem $$u'''(t)+ \lambda a(t)f\bigl(u(t)\bigr)=0,\quad 0<t<1,\quad u(0)=u'(0)=u''(1)=0,$$ where $\lambda$ is a positive parameter. Under various assumptions on $a$ and $f$, we establish intervals of the parameter $\lambda$ which yield the existence of at least one, at least two, and infinitely many positive solutions of the boundary value problem by using Krasnoselskii’s fixed-point theorem of cone expansion-compression type.

MSC:
34B18Positive solutions of nonlinear boundary value problems for ODE
34B15Nonlinear boundary value problems for ODE
34B24Sturm-Liouville theory
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References:
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