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Zbl 1072.34014
Infante, Gennaro; Webb, J.R.L.
Positive solutions of some nonlocal boundary value problems.
(English)
[J] Abstr. Appl. Anal. 2003, No. 18, 1047-1060 (2003). ISSN 1085-3375; ISSN 1687-0409/e

For two 4-point BVP $$u''(t)+g(t)f(u(t))=0\quad \text{a.e. on }[0,1],$$ $$u'(0)=0,\quad u(1)=\alpha_1u(\eta_1)+\alpha_2u(\eta_2),$$ or $$u(0)=0,\quad u(1)=\alpha_1u(\eta_1)+\alpha_2u(\eta_2),$$ the authors determine a region in the $(\alpha_1,\,\alpha_2)$-plane which ensures the existence of positive solutions. Further, they conclude that one can obtain the existence of positive solutions for an $m$-point boundary value problem under the weaker assumption that all parameters occurring in the boundary conditions are not required to be positive. Hence, their results allow more general behavior on $f$ than being either sub- or superlinear.
[Ruyun Ma (Lanzhou)]
MSC 2000:
*34B10 Multipoint boundary value problems
34B18 Positive solutions of nonlinear boundary value problems
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
34B15 Nonlinear boundary value problems of ODE

Keywords: m-point boundary value problem; positive solutions; existence

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