Positive Solutions for Second-Order Nonlinear Ordinary Differential Systems with Two Parameters

By using fixed-point theorem and under suitable conditions, we investigate the existence and multiplicity positive solutions to the following systems: u′′(t)+au(t)+bv(t)+  λh1(t)f(u(t),v(t))=0, t∈[0,1],  v′′(t)+cu(t)+dv(t)+μh2(t)g(u(t),v(t))=0,  t∈[0,1],  u(0)=u(1)=0,  v(0)=v(1)=0, where a,b,c,d are...

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Published in:ISRN applied mathematics 2011-12, Vol.2011 (2011), p.1-13
Main Authors: Sun, Lan, An, Yukun, Jiang, Min
Format: Article
Language:English
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Summary:By using fixed-point theorem and under suitable conditions, we investigate the existence and multiplicity positive solutions to the following systems: u′′(t)+au(t)+bv(t)+  λh1(t)f(u(t),v(t))=0, t∈[0,1],  v′′(t)+cu(t)+dv(t)+μh2(t)g(u(t),v(t))=0,  t∈[0,1],  u(0)=u(1)=0,  v(0)=v(1)=0, where a,b,c,d are four positive constants and λ>0, μ>0, f(u,v),g(u,v)∈C(R+×R+,R+) and h1,h2∈C([0,1],R+). We derive two explicit intervals of λ and μ, such that the existence and multiplicity of positive solutions for the systems is guaranteed.
ISSN:2090-5564
2090-5572
DOI:10.5402/2011/612591