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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.

##### MSC:
 34G10 Linear ODE in abstract spaces 35J25 Second order elliptic equations, boundary value problems 35J40 Higher order elliptic equations, boundary value problems 34B15 Nonlinear boundary value problems for ODE
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##### References:
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