Monotone Operator Methods for a Class of Nonlocal Multi-Phase Variable Exponent Problems

Mustafa Avci

doi:10.1007/s10440-026-00768-8

Monotone Operator Methods for a Class of Nonlocal Multi-Phase Variable Exponent Problems

Mustafa Avci

Centre for Science

Research output: Contribution to journal › Journal Article › peer-review

1 Citation (Scopus)

Abstract

In this paper, we study a class of nonlocal multi-phase variable exponent problems within the framework of a newly introduced Musielak-Orlicz Sobolev space. We consider two problems, each distinguished by the type of nonlinearity it includes. To establish the existence of at least one nontrivial solution for each problem, we employ two different monotone operator methods.

Original language	English
Article number	7
Journal	Acta Applicandae Mathematicae
Volume	201
Issue number	1
DOIs	https://doi.org/10.1007/s10440-026-00768-8
Publication status	Published - Feb 2026

Keywords

Multi-phase operator
Musielak-Orlicz Sobolev space
Nonlocal problem
Variable exponents

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10.1007/s10440-026-00768-8

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title = "Monotone Operator Methods for a Class of Nonlocal Multi-Phase Variable Exponent Problems",

abstract = "In this paper, we study a class of nonlocal multi-phase variable exponent problems within the framework of a newly introduced Musielak-Orlicz Sobolev space. We consider two problems, each distinguished by the type of nonlinearity it includes. To establish the existence of at least one nontrivial solution for each problem, we employ two different monotone operator methods.",

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AB - In this paper, we study a class of nonlocal multi-phase variable exponent problems within the framework of a newly introduced Musielak-Orlicz Sobolev space. We consider two problems, each distinguished by the type of nonlinearity it includes. To establish the existence of at least one nontrivial solution for each problem, we employ two different monotone operator methods.

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KW - Musielak-Orlicz Sobolev space

KW - Nonlocal problem

KW - Variable exponents

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Monotone Operator Methods for a Class of Nonlocal Multi-Phase Variable Exponent Problems

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