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J. Korean Math. Soc. 2010; 47(4): 845-860
Printed July 1, 2010
https://doi.org/10.4134/JKMS.2010.47.4.845
Copyright © The Korean Mathematical Society.
The Nehari manifold approach for Dirichlet problem involving the $p(x)$-Laplacian equation
Rabil A. Mashiyev, Sezai Ogras, Zehra Yucedag, and Mustafa Avci
Dicle University
In this paper, using the Nehari manifold approach and some variational techniques, we discuss the multiplicity of positive solutions for the $p(x)$-Laplacian problems with non-negative weight functions and prove that an elliptic equation has at least two positive solutions.
Keywords: variable exponent Lebesgue-Sobolev spaces, $p(x)$-Laplacian, variational methods, Nehari manifold, multiple positive solutions
MSC numbers: 35B38, 35D05, 35J60, 35J70, 58E05
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