We consider the equation for a class of quasilinear elliptic operators containing
-Laplacian
and mean curvature operator with the Robin boundary condition in a bounded domain
of
. Under the hypothesis
with the variable exponent
in
, we
show the existence of two or three weak solutions of the equation according to some
conditions on given functions. Our strategies are using a variant of Ricceri’s
variational principle obtained by Fan and Deng and using a mountain pass lemma by
Willem without the (PS) condition.
Keywords
$p(\cdot)$-Laplacian type operator, mean curvature
operator, Robin boundary value problem, variable exponent
Sobolev space
