Electron. J. Differential Equations, Vol. 2022 (2022), No. 24, pp. 1-16.

Multiple solutions for p(x)-Kirchhoff type problems with Robin boundary conditions

Ghasem A. Afrouzi, Nguyen Thanh Chung, Zohreh Naghizadeh

This article considers p(x)-Kirchhoff type problems with Robin boundary conditions. Using the mountain pass theorem, the Ekeland's variational principle, and Krasnoselskii's genus theory, we prove that the problem has at least two nontrivial weak solutions or infinitely many nontrivial weak solutions under some suitable conditions on the nonlinearities. The main results improve and generalize the previous ones introduced in [2,7].

Submitted May 11, 2021. Published March 25, 2022.
Math Subject Classifications: 35J70, 35J60, 35D05.
Key Words: p(x)-Kirchhoff type problems; Robin boundary conditions; variational methods.

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Ghasem A. Afrouzi
Department of Mathematics
Faculty of Mathematical Sciences
University of Mazandaran, Babolsar, Iran
email: afrouzi@umz.ac.ir
Nguyen Thanh Chung
Department of Mathematics
Quang Binh University
312 Ly Thuong Kiet
Dong Hoi, Quang Binh, Vietnam
email: ntchung82@yahoo.com
Zohreh Naghizadeh
Faculty of Sciences
Department of Mathematics
University of Science and Technology of Mazandaran
P.O. Box 48518-78195, Behshahr, Iran
email: z.naghizadeh@mazust.ac.ir

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