Positive solution to a singular $(k,n-k)$ conjugate boundary value problem

Qingliu Yao

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Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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Existence principles for solutions of singular differential systems ${(φ (u^{'}))}^{'} = f (t, u, u^{'})$ satisfying nonlocal boundary conditions are stated. Here $φ$ is a homeomorphism $ℝ^{N}$ onto $ℝ^{N}$ and the Carathéodory function $f$ may have singularities in its space variables. Applications of the existence principles are given.