What question did this study set out to answer?

The main aim is to establish the well-posedness of a nonlocal boundary value problem under a specific condition.

April 7, 2026

On the Well-Posedness of the Nonlocal BVP with the Samarskii–Ionkin Condition for Elliptic Differential Equations

Key Points

The main aim is to establish the well-posedness of a nonlocal boundary value problem under a specific condition.
Investigated a nonlocal boundary value problem (BVP) for elliptic equations in a Banach space.
Utilized the Samarskii–Ionkin condition in the analysis.
Proven coercive stability estimates for solutions.
Demonstrated well-posedness for the formulated nonlocal BVP.
Provided stability estimates for solutions to three types of nonlocal BVPs.

Abstract

In this paper, we investigate a nonlocal boundary value problem (BVP) with the Samarskii–Ionkin condition for elliptic equations (EEs) in a Banach space involving a positive operator. The main result establishes the well-posedness of the problem. Additionally, coercive stability estimates are proven for solutions to three types of nonlocal BVPs with the Samarskii–Ionkin condition for EEs.

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