The Eigenvalue Problem for p(x)-Laplacian Equations Involving Robin Boundary Condition

作     者：Lujuan YU Fengquan LI Fei XU 

作者机构：School of Mathematical Sciences Dalian University of Technology 

出 版 物：《Journal of Mathematical Research with Applications》 (数学研究及应用(英文))

年 卷 期：2018年第38卷第1期

页      面：63-76页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11571057) 

主　　题：variable exponents eigenvalue Robin boundary condition p(x)-Laplacian equations 

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 infinitely 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.