Positive Solutions for Operator Equations System and Applications toSemi-Positone Differential System

XU Xi'an

Journal of Systems Science and Mathematical Sciences ›› 2008, Vol. 28 ›› Issue (4) : 468-481.

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Journal of Systems Science and Mathematical Sciences ›› 2008, Vol. 28 ›› Issue (4) : 468-481. DOI: 10.12341/jssms10098
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Positive Solutions for Operator Equations System and Applications toSemi-Positone Differential System

  • XU Xi'an
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Abstract

In this paper, the existence of positive solutions for the operator equation system
{x=λK1F1(x,y),y=λK2F2(x,y),
is considered, where λ>0 is a parameter, P is a total cone of the real Banach space E. Under some superlinear conditions it is shown that there exists λ∗>0 such that the operator equation system has at least one positive solution for 0<λ≤λ∗. As an application,
the existence of positive solutions of a semi-positone differential boundary value system is investigated.

Key words

Semi-positive operator equation system / the fixed point index / positive solutions.

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XU Xi'an. Positive Solutions for Operator Equations System and Applications toSemi-Positone Differential System. Journal of Systems Science and Mathematical Sciences, 2008, 28(4): 468-481 https://doi.org/10.12341/jssms10098
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