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http://dx.doi.org/10.11568/kjm.2014.22.3.395

EXISTENCE OF A POSITIVE INFIMUM EIGENVALUE FOR THE p(x)-LAPLACIAN NEUMANN PROBLEMS WITH WEIGHTED FUNCTIONS  

Kim, Yun-Ho (Department of Mathematics Education Sangmyung University)
Publication Information
Korean Journal of Mathematics / v.22, no.3, 2014 , pp. 395-406 More about this Journal
Abstract
We study the following nonlinear problem $-div(w(x){\mid}{\nabla}u{\mid}^{p(x)-2}{\nabla}u)+{\mid}u{\mid}^{p(x)-2}u={\lambda}f(x,u)$ in ${\Omega}$ which is subject to Neumann boundary condition. Under suitable conditions on w and f, we give the existence of a positive infimum eigenvalue for the p(x)-Laplacian Neumann problem.
Keywords
p(x)-Laplacian; Neumann boundary condition; Weighted variable exponent Lebesgue-Sobolev spaces; Weak solution; Eigenvalue;
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