The Eigenvalue Problem for p(x)-Laplacian Equations Involving Robin Boundary Condition
Received:May 01, 2017  Revised:September 22, 2017
Key Word: Variable exponents   Eigenvalue   Robin boundary condition   p(x)-Laplacian e- quations.  
Fund ProjectL:The National Natural Science Foundation of China (Grant No.11571057).
Author NameAffiliationE-mail
Lujuan Yu Dalian University of Technology yulujuan87@mail.dlut.edu.cn 
Fengquan Li Dalian University of Technology fqli@dlut.edu.cn 
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Abstract:
      This paper studies the eigenvalue problem for p(x)-Laplacian equations involving Robin boundary condition. We obtain the Euler-Lagrange equation for the minimization of the Rayleigh quotient involving Luxemburg norms in the framework of variable exponent Sobolev space. Using the Ljusternik-Schnirelman principle, for the Robin boundary value problem, we prove the existence of in nitely many eigenvalue sequences and also show that, the smallest eigenvalue exists and is strictly positive, and all eigenfunctions associated with the smallest eigenvalue do not change sign.
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