Existence of three solutions for a Navier boundary value problem involving the \(p(x)\)-biharmonic operator. (English) Zbl 1288.35247
Authors’ abstract: The existence of at least three weak solutions is established for a class of quasilinear elliptic equations involving the \(p(x)\)-biharmonic operator with Navier boundary value conditions. The proof is mainly based on a three critical points theorem due to B. Ricceri [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 9, 3084–3089 (2009; Zbl 1214.47079)].
Reviewer: Hans-Christoph Grunau (Magdeburg)
MSC:
35J60 | Nonlinear elliptic equations |
35J40 | Boundary value problems for higher-order elliptic equations |
35A01 | Existence problems for PDEs: global existence, local existence, non-existence |