The boundary layer problem for certain non-linear ordinary differential equations
Compositio Mathematica, Tome 11 (1953), pp. 119-169. 
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     author = {Bergmann, Howard G.},
     title = {The boundary layer problem for certain non-linear ordinary differential equations},
     journal = {Compositio Mathematica},
     pages = {119--169},
     publisher = {Kraus Reprint},
     volume = {11},
     year = {1953},
     mrnumber = {58060},
     zbl = {0053.38602},
     language = {en},
     url = {http://www.numdam.org/item/CM_1953__11__119_0/}
}
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Bergmann, Howard G. The boundary layer problem for certain non-linear ordinary differential equations. Compositio Mathematica, Tome 11 (1953), pp. 119-169. http://www.numdam.org/item/CM_1953__11__119_0/

K.O. Friedrichs and J.J. Stoker [1] The Non-linear Boundary Value Problem of the Buckled Plate, American Journal of Mathematics, V. LXIII, 4, October, 1941. | JFM | MR | Zbl

Courant-Hilbert [2] Methoden der Mathematischen Physik. | JFM | Zbl

Edward Mcshane [3] Integration.

Richard Courant [4] Differential and Integral Calculus.

E.W. Hobson [5] Theory of Functions of a Real Variable.