Vol. 17, No. 2, 1966

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Boundary value problems for nonlinear ordinary differential equations

Henry A. Antosiewicz

Vol. 17 (1966), No. 2, 191–197

Conditions are given under which a quasi-linear differential equation has at least one solution in a given compact interval that satisfies a given system of homogeneous or nonhomogeneous linear constraints. These conditions are not formulated in the space in which the solutions take their values, as is usually done; instead they involve the set of continuous mappings subject to the constraints and the set of forcing terms for which the associated nonhomogeneous linear differential equation has solutions satisfying the constraints. The latter set is, under mild conditions, a topological direct summand of the space of continuous mappings. This occurs in the problem of the existence of periodic solutions which is discussed in detail as illustration.

Mathematical Subject Classification
Primary: 34.36
Received: 6 January 1965
Published: 1 May 1966
Henry A. Antosiewicz