Original scientific paper

https://doi.org/10.64785/mc.31.1.3

Existence of three solutions to a \( p(\cdot )\)- biharmonic problem via a local mountain pass theorem

Ghasem Afrouzi ; Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
John R. Graef orcid.org/0000-0002-8149-4633 ; University of Tennessee at Chattanooga, Chattanooga, USA *
A. R. Jalali ; Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

* Corresponding author.

Abstract

The authors consider the problem of the existence of multiple weak solutions to 𝑝(𝑥)-biharmonic equations
with Navier boundary conditions. Using Ricceri’s variational principle and a local mountain pass theorem, and without
requiring the Palais-Smale condition, the authors establish sufficient conditions for the existence of at least three solutions
to the problem.

Keywords

p(x)-biharmonic; Neumann problem; embedding theorem; variational methods

Hrčak ID:

345976

URI

https://hrcak.srce.hr/345976

Publication date:

2.4.2026.

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