Research Article

Effects of nonlocal source terms on Kirchhoff-type double phase equations with variable exponents: Existence of three distinct solutions

Published in: Quaestiones Mathematicae
Volume 49 , issue 6 , 2026 , pages: 801–821

DOI: 10.2989/16073606.2026.2624507

Author(s): Khaled Kefi Center for Scientific Research and Entrepreneurship, Northern Border University, Saudi Arabia , Haikel Ouerghi Department of Quantitative Methods, Jendouba University, Research Laboratory of Mathematics and Applications, Tunisia , Khaled Benali Department of Mathematics, Faculty of Sciences of Gabes, Research Laboratory of Mathematics and Applications, Tunisia , Nguyen Thanh Chung Faculty of Mathematics and Information Technology, The University of Danang - University of Science and Education, Vietnam

Keywords: 35J60 , 35D30 , 35J70 , 35A15 , 03H10 , Kirchhoff-type double phase problems , nonlocal source terms , variable exponents , Musielak-Orlicz Sobolev spaces , critical point theory

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Abstract

This paper investigates a class of Kirchhoff-type double phase problems distinguished by the inclusion of two nonlocal source terms and formulated in the framework of variable exponent Sobolev spaces. By applying a variant of Bonanno’s critical point theorem [12], we establish the existence of at least three distinct solutions. These results not only enhance the current understanding of double phase equations exhibiting sublinear growth but also extend several recent developments by incorporating variable exponents and nonlocal effects into the analysis.

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