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

The authors consider the problem of the existence of multiple weak solutions to ????(????)-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.