Positive solutions for systems of nth order three-point nonlocal boundary value problems

J. Henderson, Baylor University, Waco, Texas, U.S.A.
S. K. Ntouyas, University of Ioannina, Ioannina, Greece

E. J. Qualitative Theory of Diff. Equ., No. 18. (2007), pp. 1-12.

Abstract: Intervals of the parameter $\lambda$ are determined for which there exist positive solutions for the system of nonlinear differential equations, $u^{(n)} + \lambda a(t) f(v) = 0, \ v^{(n)} +\lambda b(t) g(u) = 0, $ for $0 < t <1$, and satisfying three-point nonlocal boundary conditions, $u(0) = 0, u'(0) = 0, \ldots, u^{(n-2)}(0) = 0, \ u(1)=\alpha u(\eta), v(0) = 0, v'(0) = 0, \ldots, v^{(n-2)}(0) = 0, \ v(1)=\alpha v(\eta)$. A Guo-Krasnosel'skii fixed point theorem is applied.

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