On the \(p\)-biharmonic operator with critical Sobolev exponent and nonlinear Steklov boundary condition. (English) Zbl 1390.35216

El Khalil, Abdelouahed; Alaoui, My Driss Morchid; Touzani, Abdelfattah

Int. J. Anal. 2014, Article ID 498386, 8 p. (2014).

Summary: We show that this operator possesses at least one nondecreasing sequence of positive eigenvalues. A direct characterization of the principal eigenvalue (the first one) is given that we apply to study the spectrum of the \(p\)-biharmonic operator with a critical Sobolev exponent and the nonlinear Steklov boundary conditions using variational arguments and trace critical Sobolev embedding.

MSC:

35P30	Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
35G30	Boundary value problems for nonlinear higher-order PDEs

Keywords:

\(p\)-biharmonic operator; fourth-order Steklov boundary problem; nondecreasing sequence of positive eigenvalues; critical Sobolev exponent