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We deal with the following system of coupled asymmetric oscillators \[\begin{cases} \ddot{x}_1+a_1x_1^+-b_1x^-_1+\phi_1(x_2)=p_1(t) \\\ddot{x}_2+a_2\,x_2^+-b_2\,x^-_2+\phi_2(x_1)=p_2(t) \end{cases} \] where$\phi_i: \mathbb{R} \to \mathbb{R}$ is locally Lipschitz continuous andbounded, $p_i: \mathbb{R} \to \mathbb{R}$ is continuous and $2\pi$-periodic andthe positive real numbers $a_i, b_i$ satisfy $$\dfrac{1}{\sqrt{a_i}}+\dfrac{1}{\sqrt{b_i}}=\dfrac{2}{n}, \quad \mbox{ for some} n \in \mathbb{N}. $$ We define a suitable function $L: \mathbb{T}^2 \to\mathbb{R}^2$, appearing as the higher-dimensional generalization of the wellknown resonance function used in the scalar setting, and we show how unboundedsolutions to the system can be constructed whenever $L$ has zeros with aspecial structure. The proof relies on a careful investigation of the dynamicsof the associated (four-dimensional) Poincar\'e map, in action-anglecoordinates.

Unbounded solutions to a system of coupled asymmetric oscillators at resonance