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A note on the Bitsadze-Samarskii type nonlocal boundary value problem in a Banach space. (English) Zbl 1154.34026
The author studies a boundary value problem for a second-order differential equation in a Banach space. Well-posedness results and coercive type estimates for solutions are obtained in suitable Hölder spaces. As applications, three boundary value problems for elliptic equations are considered.

34G10Linear ODE in abstract spaces
35J25Second order elliptic equations, boundary value problems
35J40Higher order elliptic equations, boundary value problems
34B15Nonlinear boundary value problems for ODE
Full Text: DOI
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