Min-max level estimate for a singular quasilinear polyharmonic equation in \(\mathbb R^{2m}\) (Q1939303)

The equation \((-\Delta )^m u +\sum_{k =0}^{m-1} \nabla^k \cdot (a_k (x) \nabla^k u) =f(x,u) |x|^{-\beta }+\epsilon h(x)\) is studied in \(\mathbb{R}^{2m}\). Here \(m\geq 2\) is an even integer. The authors find sufficient conditions for the existence of at least two distinct weak solutions of the equation for \(0<\epsilon <\epsilon_0\).