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Zbl 1152.34325
Graef, John R.; Yang, Bo
Multiple positive solutions to a three point third order boundary value problem. (English)
[J] Discrete Contin. Dyn. Syst. 2005, Suppl., 337-344 (2005). ISSN 1078-0947; ISSN 1553-5231/e

Summary: The authors consider the boundary value problem $$u'''(t)= q(t)f(u), \quad 0<t<1, \qquad u(0)= u'(p)= u''(1)=0,$$ where $p\in (\frac12,1)$ is a constant. They give sufficient conditions for the existence of multiple positive solutions to this problem. In so doing, they are able to improve some recent results on this problem. Examples are included to illustrate the results.

MSC 2000:: *34B18 Positive solutions of nonlinear boundary value problems
34B15 Nonlinear boundary value problems of ODE
34B10 Multipoint boundary value problems
47N20 Appl. of operator theory to differential and integral equations

Keywords: boundary value problems; existence of positive solutions; nonexistence of positive solutions; nonlinear equations; three point problems; third order equations

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