TY - JOUR
T1 - Eigenvalue Problem for a Class of Quasilinear Elliptic Operators with Mixed Boundary Value Condition in a Variable Exponent Sobolev Space
AU - Aramaki , Junichi
JO - Communications in Mathematical Research 
VL - 4
SP - 437
EP - 481
PY - 2024
DA - 2024/12
SN - 40
DO - http://doi.org/10.4208/cmr.2024-0039
UR - https://global-sci.org/intro/article_detail/cmr/23701.html
KW - Eigenvalue problem, $p(·)$-Laplacian type equation, mean curvature operator,
mixed boundary value problem.
AB - <p style="text-align: justify;">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.</p>