A mixed-dispersion equation in dimension 4: results and open problems

I will present results concerning the existence of unbounded sequences of solutions, obtained via variational methods, to an elliptic mixed-dispersion equation in dimension 4, in the so-called positive-mass and zero-mass cases. Specific symmetries are used to recover compactness and, in the latter case, even to ensure the energy functional is continuously differentiable. I will also present an open problem about the zero-mass case.