Dirichlet and Neumann eigenvalue problems on CR manifolds

2018 ◽  
Vol 67 (2) ◽  
pp. 285-320 ◽  
Author(s):  
Amine Aribi ◽  
Sorin Dragomir
Keyword(s):  
Eigenvalue Problems ◽  
Cr Manifolds ◽  
Neumann Eigenvalue

scholarly journals Nonlinear nonhomogeneous Neumann eigenvalue problems

2015 ◽  
pp. 1-24 ◽  
Author(s):  
Pasquale Candito ◽  
Roberto Livrea ◽  
Nikolaos Papageorgiou
Keyword(s):  
Eigenvalue Problems ◽  
Neumann Eigenvalue

scholarly journals Multiple solutions for a class of nonlinear Neumann eigenvalue problems

2014 ◽  
Vol 13 (4) ◽  
pp. 1491-1512 ◽  
Author(s):  
Leszek Gasiński ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Multiple Solutions ◽  
Eigenvalue Problems ◽  
Neumann Eigenvalue

scholarly journals A Bifurcation-Type Result for Nonlinear Neumann Eigenvalue Problems

2012 ◽  
Vol 55 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Sophia Th. Kyritsi ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Eigenvalue Problems ◽  
Type Result ◽  
Neumann Eigenvalue

scholarly journals Neumann eigenvalue problems on the exterior domains

2019 ◽  
Vol 187 ◽  
pp. 339-351
Author(s):  
T.V. Anoop ◽  
Nirjan Biswas
Keyword(s):  
Eigenvalue Problems ◽  
Exterior Domains ◽  
Neumann Eigenvalue

scholarly journals Eigenvalue bounds of mixed Steklov problems

2019 ◽  
Vol 22 (02) ◽  
pp. 1950008 ◽  
Author(s):  
Asma Hassannezhad ◽  
Ari Laptev
Keyword(s):  
Eigenvalue Problem ◽  
Fractional Laplacian ◽  
Eigenvalue Problems ◽  
Asymptotic Results ◽  
Riesz Means ◽  
Dirichlet Eigenvalue ◽  
Eigenvalue Bounds ◽  
Steklov Eigenvalue ◽  
Dirichlet Eigenvalue Problem ◽  
Neumann Eigenvalue

We study bounds on the Riesz means of the mixed Steklov–Neumann and Steklov–Dirichlet eigenvalue problem on a bounded domain [Formula: see text] in [Formula: see text]. The Steklov–Neumann eigenvalue problem is also called the sloshing problem. We obtain two-term asymptotically sharp lower bounds on the Riesz means of the sloshing problem and also provide an asymptotically sharp upper bound for the Riesz means of mixed Steklov–Dirichlet problem. The proof of our results for the sloshing problem uses the average variational principle and monotonicity of sloshing eigenvalues. In the case of Steklov–Dirichlet eigenvalue problem, the proof is based on a well-known bound on the Riesz means of the Dirichlet fractional Laplacian, and an inequality between the Dirichlet and Navier fractional Laplacian. The two-term asymptotic results for the Riesz means of mixed Steklov eigenvalue problems are discussed in the Appendix which in particular show the asymptotic sharpness of the bounds we obtain.

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