Differential and Integral Equations

Fredholm mappings and the generalized boundary value problem

V. Šeda

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The generalized boundary value problem (BVP for short) for $n$-th order ordinary differential equations generates a mapping from a Banach space into another Banach space which mapping in most cases is the sum of a Fredholm mapping of index $0$ and of a completely continuous mapping. The properties of such mappings are very thoroughly studied in the paper, especially generic properties, surjectivity and the bifurcation problem. Applications to the generalized BVP are given and in the case when the corresponding ar homogeneous BVP is positive or self-adjoint some new results have been derived.

Article information

Differential Integral Equations, Volume 8, Number 1 (1995), 19-40.

First available in Project Euclid: 21 May 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47H15
Secondary: 34B15: Nonlinear boundary value problems 47N20: Applications to differential and integral equations 58B15: Fredholm structures [See also 47A53] 58C15: Implicit function theorems; global Newton methods


Šeda, V. Fredholm mappings and the generalized boundary value problem. Differential Integral Equations 8 (1995), no. 1, 19--40. https://projecteuclid.org/euclid.die/1369143782

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