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Open Access Research Article

On the existence of solutions of boundary value problems for quasilinear elliptic equations of general form in Sobolev spaces

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pp. 1941–1954Vol. 28Issue 5August 2025DOI: 10.47974/JIM-2182XML
Received:
17 Aug 2024
Published Online:
19 Aug 2025
Article type:
Research Article
Language:
EN
Article no.:
JIM-2182
Pages:
1941–1954

Abstract

The aim of the study is to prove the existence of functions satisfying a quasilinear elliptic equation of general form and satisfying the given boundary conditions in Sobolev spaces. Methods of functional analysis, theory of functions of many variables, differential calculus of functions were used to achieve this goal. The main results of the study include the formulation and proof of the theorem on the existence of solutions of boundary value problems for quasilinear elliptic equations of general form in Sobolev spaces. A general methodology has been developed to prove the existence of solutions for a wide class of quasilinear elliptic equations. 

Keywords

Subject Classifications

35J6235J6646E35

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