In this article, we investigate the existence and nonexistence of weak solutions to higher-order doubly critical elliptic problems with weights, driven by a polyharmonic double phase operator. More precisely, we deal with the following problem \(\begin{aligned} {\left\{ \begin{array}{ll} \mathcal {L}^m_{p,q}(u) = f(x,u) ~& \text {in } \Omega ,\\ u=\nabla u=\cdots \nabla ^{m-1} u=0 & \text {on }{\partial \Omega }, \end{array}\right. } \end{aligned}\) where \(\Omega \subset \mathbb {R}^N\) with \(N \ge 2\) is a smooth bounded domain with Lipschitz boundary \(\partial \Omega \) , \(m \in \mathbb {N}\) , \(1< p< q < \frac{N}{m}\) with \((N-1)q\le Np\) , the nonlinear term \(f:\Omega \times \mathbb {R}\rightarrow \mathbb {R}\) is a Carathéodory function, which has doubly critical growth, and \(\mathcal {L}^m_{p,q}\) represents a polyharmonic double phase operator. By establishing new compactness results within a suitable Musielak–Orlicz–Sobolev framework and applying variational methods, we prove the existence of nontrivial weak solutions. In addition, we derive nonexistence results under appropriate assumptions by establishing a Pohozaev-type identity for higher-order derivatives. Our approach extends classical techniques to capture the intricate features of the double-phase operator for higher-order derivatives, and addresses the difficulties arising from critical nonlinearities, in particular extending the results of [F. Colasuonno, K. Perera, J. Differ. Equ., 422 (2025), 426–488] in a polyharmonic double phase setup overcoming the non-closedness of truncations in higher-order Sobolev spaces.
