Division of Science
Faculty of Science and Engineering
Tokyo Denki University,
Hatoyama-machi, Saitama 350-0394, Japan
email: aramaki@hctv.ne.jp
Junichi Aramaki
Abstract:
In this article, we consider an eigenvalue problem for the Kirchhoff-type
equation containing p(.)-Laplacian and the 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 an another part of the boundary.
We show that the eigenvalue problem has infinitely many eigenpairs by
using the celebrated Ljusternik-Schnirelmann principle in the calculus of
variation. Moreover, we derive that in a variable exponent Sobolev space,
there are two cases where the infimum of all eigenvalues is equal to
zero and is positive.
Submitted April 21, 2024. Published February 25, 2025.
Math Subject Classifications: 49R50, 35A01, 35J62, 35J57.
Key Words: Eigenvalue problem; Kirchhoff-type operator; p(.)-Laplacian;
mean curvature operator; mixed boundary value problem; variable exponent Sobolev space.
DOI: 10.58997/ejde.2025.17
Show me the PDF file (497 KB), TEX file for this article.
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Junichi Aramaki Division of Science Faculty of Science and Engineering Tokyo Denki University, Hatoyama-machi, Saitama 350-0394, Japan email: aramaki@hctv.ne.jp |
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