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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:
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34B24 Sturm-Liouville theory
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