Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

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

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Journal Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]