Geodesic
Nonlinear boundary value problems for second order systems with one-sided growth constraints of the right side with respect to the first derivatives
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part 8, Tome 159 (1987), pp. 156-175

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For system of integrodifferential equation $u_i^{\prime\prime}+Q_i(t)u^\prime_i+R_i(t)u_i=f_i(t,u_1,\dots,u_n,u_1^\prime,\dots,u_n^\prime,\int_0^1k_i(t,s,u_1(s),\dots,u_n(s))ds)$ $(i=1,\dots,n)$ we establish existence theorems for the solutions of the problem with boundary conditions $a_iu_i(0)-b_iu_i^\prime(0)=q_i\varphi_i(u_1(0),\dots,u_n(0),u_1(1),\dots,u_n(1),\int_0^1\ell_i(s,u_1(s),\dots,u_n(s))ds)$; $ c_iu_i(1)+d_iu_1^\prime(1)=h_i\Psi_i(u_1(0),\dots,u_n(0),u_1(1),\dots,u_n(1),\int_0^1M_i(s,u_1(s),\dots,u_n(s))ds)$ $(i=1,\dots,n)$. 
@article{ZNSL_1987_159_a16,
     author = {M. N. Yakovlev},
     title = {Nonlinear boundary value problems for second order systems with one-sided growth constraints of the right side with respect to the first derivatives},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {156--175},
     publisher = {mathdoc},
     volume = {159},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_159_a16/}
}
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%A M. N. Yakovlev
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%I mathdoc
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%G ru
%F ZNSL_1987_159_a16
M. N. Yakovlev. Nonlinear boundary value problems for second order systems with one-sided growth constraints of the right side with respect to the first derivatives. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part 8, Tome 159 (1987), pp. 156-175. http://geodesic.mathdoc.fr/item/ZNSL_1987_159_a16/