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Multiplicity of positive solution of -Laplacian problems with sign-changing weight functions
-
Khaled Ben Ali
Published/Copyright:
March 27, 2012
Abstract.
This article shows the existence and multiplicity of positive solutions of the 
-Laplacian problem
where 
is a bounded open set in 
with smooth boundary and 
are continuous functions on 
such that
and 
are smooth functions which may change sign in 
. The method is based on Nehari results on three sub-manifolds of the space 
.
Keywords.: -Laplace operator; generalized Lebesgue–Sobolev spaces; variational methods; Nehari manifold; weak solution
Received: 2011-12-12
Revised: 2011-12-27
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
- Combined Sundman–Darboux transformations and solutions of nonlinear ordinary differential equations of second order
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Keywords for this article
-Laplace operator;
generalized Lebesgue–Sobolev spaces;
variational methods;
Nehari manifold;
weak solution
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
