Geodesic
Existence of solution to nonlinear boundary value problem for ordinary differential equation of the second order in Hilbert space
Mathematica Bohemica, Tome 117 (1992) no. 4, pp. 415-424.

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In this paper we deal with the boundary value problem in the Hilbert space. Existence of a solutions is proved by using the method of lower and upper solutions. It is not necessary to suppose that the homogeneous problem has only the trivial solution. We use some results from functional analysis, especially the fixed-point theorem in the Banach space with a cone (Theorem 4.1, [5]).
DOI : 10.21136/MB.1992.126059
Classification : 34B15, 34G20, 35B25, 47E05, 47N20
Keywords: boundary value problem; existence of solutions; ordinary differential equations in Hilbert space; lower and upper solution 
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Rovderová, Eva. Existence of solution to nonlinear boundary value problem for ordinary differential equation of the second order in Hilbert space. Mathematica Bohemica, Tome 117 (1992) no. 4, pp. 415-424. doi : 10.21136/MB.1992.126059. http://geodesic.mathdoc.fr/articles/10.21136/MB.1992.126059/

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