A variational approach for solving \(p(x)\)-biharmonic equations with Navier boundary conditions. (English) Zbl 1381.35036
The main goal of the authors of this work is to establish the existence of at least three weak solutions for \(p(x)\)-biharmonic equations with Navier boundary conditions. The formulation of the problem involves two parameters, \(\lambda\) (positive) and \(\mu\) (nonnegative). The article includes results on the existence of weak solutions as well as precise estimates for these parameters. The authors note that, for the existence results, no asymptotic condition at infinity is required on the nonlinear terms included in the problem formulation. They also provided an example illustrating the existence theorems and bounds for the parameters. A case with \(\mu=0\) and an autonomous right-hand side is discussed and an example for this case is given.
Reviewer: Baasansuren Jadamba (Rochester)
MSC:
| 35J40 | Boundary value problems for higher-order elliptic equations |
| 35J20 | Variational methods for second-order elliptic equations |
| 35J60 | Nonlinear elliptic equations |
| 35D30 | Weak solutions to PDEs |
| 35J35 | Variational methods for higher-order elliptic equations |
| 35J62 | Quasilinear elliptic equations |
Keywords:
\(p(x)\)-Laplace operator; variable exponent Sobolev spaces; variational method; critical point theoryReferences:
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