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A priori estimates of Nodal solutions on the annulus for some PDE and their Morse index
-
Abdellaziz Harrabi
Published/Copyright:
March 27, 2012
Abstract.
In this paper we consider radially symmetric solutions of the nonlinear Dirichlet problem 
in 
, where 
is an annulus in 
, 
,
and 
satisfies some appropriate conditions. We establish a priori estimates of radial solutions with 
prescribed number of zeros. Moreover, when 
, where 
is odd and super-linear at infinity, using the uniqueness result due to Tanaka (2007), we verify that these solutions are non-degenerate and we prove that their radial Morse index is exactly 
.
Received: 2011-11-19
Accepted: 2011-12-14
Published Online: 2012-03-27
Published in Print: 2012-April
© 2012 by Walter de Gruyter Berlin Boston
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- A priori estimates of Nodal solutions on the annulus for some PDE and their Morse index
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Articles in the same Issue
- Masthead
- Spectrum of the finite Dunkl transform operator and Donoho–Stark uncertainty principle
- A priori estimates of Nodal solutions on the annulus for some PDE and their Morse index
- Combined Sundman–Darboux transformations and solutions of nonlinear ordinary differential equations of second order
- Multiresolution analysis on local fields and characterization of scaling functions
- Multiplicity of positive solution of -Laplacian problems with sign-changing weight functions
- Small gaps Fourier series and generalized variations
- Central limit theorems for radial random walks on matrices for
