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

Abstract EN

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.