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Positive solutions for systems of nonlinear boundary value problems. (English) Zbl 1148.34016

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.

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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