On the \(p\)-biharmonic operator with critical Sobolev exponent and nonlinear Steklov boundary condition (Q1637842)
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scientific article; zbMATH DE number 6883056
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the \(p\)-biharmonic operator with critical Sobolev exponent and nonlinear Steklov boundary condition |
scientific article; zbMATH DE number 6883056 |
Statements
On the \(p\)-biharmonic operator with critical Sobolev exponent and nonlinear Steklov boundary condition (English)
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11 June 2018
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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.
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\(p\)-biharmonic operator
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fourth-order Steklov boundary problem
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nondecreasing sequence of positive eigenvalues
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critical Sobolev exponent
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