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boundary value problem; existence of solutions; ordinary differential equations in Hilbert space; lower and upper solution

References:

[1] V. Šeda: **On some non-linear boundary value problems for ordinary differential equations**. Archivum Mathematicum (Brno) 25 (1989), 207-222. MR 1188065

[2] B. Rudolf: **Periodic boundary value problem in Hilbert space for differential equation of second order with reflection to the argument**. Mathematica Slovaca 42 no. 1 (1992), 65-84. MR 1159492

[3] M. Greguš M. Švec V. Šeda: **Ordinary differential equations**. Alfa, Bratislava, 1985. (In Slovak.)

[4] G. J. Šilov: **Mathematical analysis**. (Slovak translation), Alfa, Bratislava, 1985.

[5] M. A. Krasnosel'skij: **Positive solutions of operators equations**. Gosud. izd., Moskva, 1962. (In Russian.)

[6] E. Rovderová: **A note on a Cone in the space $L_2(, H)$**. Diploma Thesis, 1990.