On the p-Biharmonic Operator with Critical Sobolev Exponent and Nonlinear Steklov Boundary Condition

الملخص EN

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.