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We prove the existence of infinitely many solutions
$u\in W_{0}^{1,2}(\unicode[STIX]{x1D6FA})$
for the Kirchhoff equation
where
$$\begin{eqnarray}\displaystyle -\biggl(\unicode[STIX]{x1D6FC}+\unicode[STIX]{x1D6FD}\int _{\unicode[STIX]{x1D6FA}}|\unicode[STIX]{x1D6FB}u|^{2}\,dx\biggr)\unicode[STIX]{x1D6E5}u=a(x)|u|^{q-1}u+\unicode[STIX]{x1D707}f(x,u)\quad \text{in }\unicode[STIX]{x1D6FA}, & & \displaystyle \nonumber\end{eqnarray}$$
$\unicode[STIX]{x1D6FA}\subset \mathbb{R}^{N}$
is a bounded smooth domain,
$a(x)$
is a (possibly) sign-changing potential,
$0
$\unicode[STIX]{x1D6FC}>0$
,
$\unicode[STIX]{x1D6FD}\geq 0$
,
$\unicode[STIX]{x1D707}>0$
and the function
$f$
has arbitrary growth at infinity. In the proof, we apply variational methods together with a truncation argument.
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