Solvability of Some Elliptic Equations with a Nonlocal Boundary Condition

Serik Aitzhanov, Bakytbek Koshanov and Aray Kuntuarova ()
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Serik Aitzhanov: Department of Mathematics, Al-Farabi Kazakh National University, Kazakhstan, Almaty, al-Farabi Ave. 71, Almaty 050040, Kazakhstan
Bakytbek Koshanov: Institute of Mathematics and Mathematical Modeling, Shevchenko Str. 28, Almaty 050010, Kazakhstan
Aray Kuntuarova: Department of Mathematics and Mathematical Modeling, Abai Kazakh National Pedagogical University, Dostyk Ave. 13, Almaty 050000, Kazakhstan

Mathematics, 2024, vol. 12, issue 24, 1-12

Abstract: In this work, we study a nonlocal boundary value problem for a quasilinear elliptic equation. Using the method of regularization and parameter continuation, we prove the existence and uniqueness of a regular solution to the nonlocal boundary value problem, i.e., a solution that possesses all generalized derivatives in the sense of S. L. Sobolev, which are involved in the corresponding equation.

Keywords: nonlocal boundary value problem; quasilinear elliptic equation; method of regularization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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