TY - JOUR
T1 - Kirchhoff-Type Problem with Mixed Boundary Condition in a Variable Exponent Sobolev Space
AU - Aramaki , Junichi
JO - Communications in Mathematical Research 
VL - 4
SP - 539
EP - 574
PY - 2023
DA - 2023/11
SN - 39
DO - http://doi.org/10.4208/cmr.2023-0017
UR - https://global-sci.org/intro/article_detail/cmr/22100.html
KW - Kirchhoff-type problem, mixed boundary value problem, $p(·)$-Laplacian
type equation, weak solutions.
AB - <p style="text-align: justify;">In this paper, we consider a mixed boundary value problem for the
stationary Kirchhoff-type equation containing $p(·)$-Laplacian. 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 the existence of at least one, two or infinitely many nontrivial weak solutions according to hypotheses on given functions.</p>