Eigenvalue Problem for a Class of Quasilinear Elliptic Operators with Mixed Boundary Value Condition in a Variable Exponent Sobolev Space
Year: 2024
Author: Junichi Aramaki
Communications in Mathematical Research , Vol. 40 (2024), Iss. 4 : pp. 437–481
Abstract
In this paper, we consider an eigenvalue problem for a class of nonlinear elliptic operators containing $p(·)$-Laplacian and mean curvature operator 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 infinitely many positive eigenvalues of the equation. Furthermore, under some conditions, we derive that the infimum of the set of all the eigenvalues becomes zero or remains to be positive.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2024-0039
Communications in Mathematical Research , Vol. 40 (2024), Iss. 4 : pp. 437–481
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 45
Keywords: Eigenvalue problem $p(·)$-Laplacian type equation mean curvature operator mixed boundary value problem.