Geodesic
Existence Principles for Singular Vector Nonlocal Boundary Value Problems with $\phi $-Laplacian and their Applications
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 50 (2011) no. 1, pp. 99-118.

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Existence principles for solutions of singular differential systems$ (\phi (u^{\prime }))^{\prime }=f(t,u,u^{\prime }) $ satisfying nonlocal boundary conditions are stated. Here $\phi $ is a homeomorphism $\mathbb {R}^N$ onto $\mathbb {R}^N$ and the Carathéodory function $f$ may have singularities in its space variables. Applications of the existence principles are given.
Classification : 34B16, 34B18, 47H11
Keywords: singular boundary value problem; system of differential equations; nonlocal boundary condition; existence principle; positive solution; $\phi $-Laplacian; Leray–Schauder degree 
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Staněk, Svatoslav. Existence Principles for Singular Vector Nonlocal Boundary Value Problems with $\phi $-Laplacian and their Applications. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 50 (2011) no. 1, pp. 99-118. http://geodesic.mathdoc.fr/item/AUPO_2011__50_1_a8/