Henderson, J.; Ntouyas, S. K. Positive solutions for systems of nonlinear boundary value problems. (English) Zbl 1148.34016 Nonlinear Stud. 15, No. 1, 51-60 (2008). Summary: Values of the parameter \(\lambda\) are determined for which there exist positive solutions of the system of boundary value problems \[ u''+\lambda a(t)f(v)=0,\;v''+\lambda b(t)g(u)=0,\text{ for }0 < t < 1 \]and satisfying \[ \alpha u(0)-\beta u'(0) = 0,\quad \gamma u(1)+\delta u'(1)=0,\quad \alpha v(0)+\beta v'(0) =0,\quad \gamma v(1)+\delta v'(1)=0. \]A well-known Guo-Krasnosel’skii fixed point theorem is applied. Cited in 25 Documents MSC: 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations PDFBibTeX XMLCite \textit{J. Henderson} and \textit{S. K. Ntouyas}, Nonlinear Stud. 15, No. 1, 51--60 (2008; Zbl 1148.34016)