TY - JOUR
T1 - On Stationary $p(·)$-Kirchhoff-Type Problem with Mixed Boundary Conditions
AU - Aramaki , Junichi
JO - Analysis in Theory and Applications
VL - 2
SP - 140
EP - 171
PY - 2025
DA - 2025/07
SN - 41
DO - http://doi.org/10.4208/ata.OA-2022-0010
UR - https://global-sci.org/intro/article_detail/ata/24280.html
KW - Mixed boundary value problem, $p(·)$-Kirchhoff-type problem, existence of a weak solution, variational methods.
AB - <p style="text-align: justify;">In this paper, we consider the stationary Kirchhoff-type equation with mixed
boundary conditions in a variable exponent Sobolev space. We show the existence of
a weak solution. Moreover, we prove the existence of a non-trivial weak solution and
infinitely many weak solutions under some hypotheses by variational methods.</p>