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Applied Mathematics

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

Published 2025-10-09

  • Ghasem Afrouzi
    • ,
  • John R. Graef
    • ,
  • A. R. Jalali

Ghasem Afrouzi
University of Mazandaran, Babolsar, Iran

John R. Graef
Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, 37403 TN, USA

A. R. Jalali
University of Mazandaran, Babolsar, Iran

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, they establish sufficient conditions for the existence of at least three solutions to the problem.

Keywords

p(x)-biharmonic, Neumann problem, Embedding theorem, Variational methods

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Author Biography

Ghasem Afrouzi

Professor of Mathematics

John R. Graef

Professor of Mathematics

A. R. Jalali

Dr. of Mathematics