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Global bifurcation result for the p-biharmonic operator
We prove isolatedness and simplicity of the first eigenvalue for the p-biharmonic operator. We also prove that the first eigenvalue is a bifurcation point for associated nonlinear boundary value problem....
BA - Obecná matematika
- 2002 •
- D
Rok uplatnění
D - Stať ve sborníku
Sharp bounds for eigenvalues of biharmonic operators with complex potentials in low dimensions
We derive sharp quantitative bounds for eigenvalues of biharmonic operators perturbed by complex-valued potentials in dimensions one, two and three....
Pure mathematics
- 2021 •
- Jimp •
- Link
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Jimp - Článek v periodiku v databázi Web of Science
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Global bifurcation result for the p-biharmonic operator
We prove that the nonlinear eigenvalue problem for the p-biharmonic operator has positive prinicpal eigenvalue which is simple and isolated. The corresponding eigenfunction is positive. We also prove that the principle eigenvalue is...
BA - Obecná matematika
- 2001 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Estimates of the principal eigenvalue of the p-biharmonic operator
We provide estimates from below and from above for the principal eigenvalue of the p-biharmonic operator on a bounded domain with the Navier boundary conditions. We apply these estimates to study the asymptotic behavior of the princ...
BA - Obecná matematika
- 2012 •
- Jx •
- Link
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Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
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Continuous dependence of eigenvalues of p-biharmonic problems on p
We are concerned with the Dirichlet and Neumann eigenvalue problem for ordinary quasilinear fourth-order (p-biharmonic) equation. We prove that the eigenvalues depend continuously on p, and that they interlace with the eigenvalues of the Nav...
BA - Obecná matematika
- 2013 •
- Jx •
- Link
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
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Asymptotics for the principal eigenvalue of the p-biharmonic operator on the ball as p approaches 1
Using the estimates of the principal eigenvalue of the p-biharmonic operator on the ball from below and from above, we provide its asymptotic analysis as p approaches 1....
BA - Obecná matematika
- 2014 •
- Jx •
- Link
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Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
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Estimates of the Principal Eigenvalue of the p-Laplacian and the p-Biharmonic Operator
We survey recent results concerning estimates of the principal eigenvalue of the Dirichlet p-Laplacian and the Navier p-biharmonic operator on a ball of radius $R$ in $R^N$ and its asymptotics for p approaching 1 and infinity....
BA - Obecná matematika
- 2015 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Pseudomodes for Biharmonic Operators with Complex Potentials
This article is devoted to the construction of pseudomodes of one-dimensional biharmonic operators with complex-valued potentials via the WKB method. As a by-product, the shape of pseudospectrum near infinity can be described. This ...
Pure mathematics
- 2023 •
- Jimp •
- Link
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Jimp - Článek v periodiku v databázi Web of Science
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Global bifurcation result for Dirichlet and Neumann p-biharmonic problem
We consider the Dirichlet and Neumann fourth-order quasilinear boundary value problem for the so-called p-biharmonic equation. We determine the Leray-Schauder degree of the associated operators. As a standard consequence, we then pr...
BA - Obecná matematika
- 2007 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Existence of two non-zero weak solutions for a p(•)-biharmonic problem with Navier boundary conditions
In this paper, the existence of non-trivial weak solutions for some problems with Navier boundary conditions driven by the p(center dot)-biharmonic operator is investigated. The proofs combine variational methods with topological ar...
Pure mathematics
- 2023 •
- Jimp •
- Link
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Jimp - Článek v periodiku v databázi Web of Science
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