Existence of solutions for an \(n\)-dimensional operator equation and applications to BVPs. (English) Zbl 1298.34118

Summary: By applying the Guo-Lakshmikantham fixed point theorem on high dimensional cones, sufficient conditions are given to guarantee the existence of positive solutions of a system of equations of the form \[ x_i(t)=\sum_{k=1}^n\sum_{j=1}^n\gamma_{ij}(t)w_{ijk}(\Lambda_{ijk} [x_k])+(F_ix)(t),\quad t\in[0,1],\quad i=1, \dots, n. \] Applications are given to three boundary value problems.


34K10 Boundary value problems for functional-differential equations
47N20 Applications of operator theory to differential and integral equations
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