Abstract
We investigate the existence of multiple solutions
for the $(p,q)$-quasilinear elliptic problem
\[
\begin{cases}
-\Delta_p u -\Delta_q u\ =\ g(x, u) + \varepsilon\ h(x,u)
& \mbox{in } \Omega,\\
u=0 & \mbox{on } \partial\Omega,\\
\end{cases}
\]
where $1< p< q< +\infty$, $\Omega$ is an open bounded domain of
${\mathbb R}^N$, the nonlinearity $g(x,u)$ behaves at infinity as $|u|^{q-1}$,
$\varepsilon\in{\mathbb R}$ and $h\in C(\overline\Omega\times{\mathbb R},{\mathbb R})$.
In spite of the possible lack of a variational structure of this problem,
from suitable assumptions on $g(x,u)$ and
appropriate procedures and estimates,
the existence of multiple solutions can be proved for small perturbations.
Publisher
Uniwersytet Mikolaja Kopernika/Nicolaus Copernicus University
Subject
Applied Mathematics,Analysis