ABSTRACT
In this article, the Ekeland variational principle, mountain pass theorem and Trudinger–Moser inequality are applied to establish the existence and multiplicity of solutions for the following nonhomogeneous Kirchhoff-type elliptic problem:
where Ω is a smooth bounded domain in
,
is a Kirchhoff function,
is a continuous function,
,
,
, and ε is a small positive parameter. The nonlinearity term
behaves like
when
for some
.
Disclosure statement
No potential conflict of interest was reported by the author(s).