The Eigenvalue Problem for p(x)-Laplacian Equations Involving Robin Boundary Condition
The Eigenvalue Problem for p(x)-Laplacian Equations Involving Robin Boundary Condition
投稿时间:2017-05-01  最后修改时间:2017-09-22
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中文关键词:  
英文关键词:Variable exponents  Eigenvalue  Robin boundary condition  p(x)-Laplacian e- quations.
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作者单位E-mail
余路娟 大连理工大学 yulujuan87@mail.dlut.edu.cn 
李风泉 大连理工大学 fqli@dlut.edu.cn 
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英文摘要:
      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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