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

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...

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Bibliographic Details
Published in:International journal of analysis 2014-01, Vol.2014 (2014), p.1-8
Main Authors: El Khalil, Abdelouahed, Alaoui, My Driss Morchid, Touzani, Abdelfattah
Format: Article
Language:English
Subjects:
Boundary conditions
Eigenvalues
Exponents
Inequality
Microelectromechanical systems
Nonlinearity
Operators
Partial differential equations
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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.
ISSN:2314-498X
2314-4998
DOI:10.1155/2014/498386