Candito, Pasquale; Molica Bisci, Giovanni Multiple solutions for a Navier boundary value problem involving the \(p\)–biharmonic operator. (English) Zbl 1258.35083 Discrete Contin. Dyn. Syst., Ser. S 5, No. 4, 741-751 (2012). This paper is concerned with multiplicity of weak solutions for the equation \(\Delta(|\Delta|^{p-2}\Delta u)=\lambda f(x,u)\) in a smooth and bounded open set \(\Omega\), subject to Navier boundary conditions. It is assumed \(p>\max\{1,N/2\}\), \(\lambda>0\) and \(f\) continuous. Using a variational approach in the spirit of Bonanno-Marano, the authors obtain the existence of three nontrivial solutions in the space \(W^{2,p}(\Omega)\cap W_0^{1,p}(\Omega)\). Reviewer: Marius Ghergu (Dublin) Cited in 14 Documents MSC: 35J40 Boundary value problems for higher-order elliptic equations 35J60 Nonlinear elliptic equations 35D30 Weak solutions to PDEs Keywords:\(p\)-biharmonic operator; multiple weak solutions; critical point theory PDFBibTeX XMLCite \textit{P. Candito} and \textit{G. Molica Bisci}, Discrete Contin. Dyn. Syst., Ser. S 5, No. 4, 741--751 (2012; Zbl 1258.35083) Full Text: DOI