Eigenvalue Problem for a Class of Quasilinear Elliptic Operators with Mixed Boundary Value Condition in a Variable Exponent Sobolev Space  

作　　者：Junichi Aramaki 

机构地区：[1]Dioision of Science,Tokyo Denki University,Hatoyama-machi,Saitama,350-0394,Japan

出　　处：《Communications in Mathematical Research》2024年第4期437-481,共45页数学研究通讯(英文版)

摘　　要：In this paper,we consider an eigenvalue problem for a class of non-linear elliptic operators containing p(-)-Laplacian and mean curvature opera-tor with mixed boundary conditions.More precisely,we are concerned with the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on another part of the boundary.Using the Ljusternik-Schnirelmann variational method,we show the existence of infini-tely many positive eigenvalues of the equation.Furthermore,under some con-ditions,we derive that the infimum of the set of all the eigenvalues becomes zero or remains to be positive.

关 键 词：Eigenvalue problem p(·)-Laplacian type equation mean curvature operator 

分 类 号：O17[理学—数学]