  In this paper we study the following nonlocal Dirichlet equation of double
phase type
  \begin{align*}
  -\psi \left [ \int_\Omega \left ( \frac{|\nabla u |^p}{p} + \mu(x)
\frac{|\nabla u|^q}{q}\right)\,\mathrm{d} x\right] \mathcal{G}(u) = f(x,u)\quad
\text{in } \Omega, \quad u = 0\quad \text{on } \partial\Omega,
  \end{align*}
  where $\mathcal{G}$ is the double phase operator given by
  \begin{align*}
  \mathcal{G}(u)=\operatorname{div} \left(|\nabla u|^{p-2}\nabla u + \mu(x)
|\nabla u|^{q-2}\nabla u \right)\quad u\in W^{1,\mathcal{H}}_0(\Omega),
  \end{align*}
  $\Omega\subseteq \mathbb{R}^N$, $N\geq 2$, is a bounded domain with Lipschitz
boundary $\partial\Omega$, $1<p<N$, $p<q<p^*=\frac{Np}{N-p}$, $0 \leq
\mu(\cdot)\in L^\infty(\Omega)$, $\psi(s) = a_0 + b_0 s^{\vartheta-1}$ for
$s\in\mathbb{R}$, with $a_0 \geq 0$, $b_0>0$ and $\vartheta \geq 1$, and
$f\colon\Omega\times\mathbb{R}\to\mathbb{R}$ is a Carath\'{e}odory function
that grows superlinearly and subcritically. We prove the existence of two
constant sign solutions (one is positive, the other one negative) and of a
sign-changing solution which turns out to be a least energy sign-changing
solution of the problem above. Our proofs are based on variational tools in
combination with the quantitative deformation lemma and the
Poincar\'{e}-Miranda existence theorem.
