Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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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)
  • Received : 2014.05.01
  • Accepted : 2014.07.09
  • Published : 2014.09.30
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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.

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References

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