Unbounded solutions to systems of differential equations at resonance

Alberto Boscaggin, Walter Dambrosio, Duccio Papini

We deal with a weakly coupled system of ODEs of the type $$x_j^{\prime \prime }+n_j^2{x}_j+h_j(x_1,\dots ,x_d)=p_j(t),j=1,\dots ,d,$$ with $h_j$ locally Lipschitz continuous and…