Minimax characterization of solutions for a semilinear elliptic equation with lack of compactness (Q1325252)

Conditions ensuring bifurcation from any boundary point of the spectrum are studied for a class of nonlinear operators. The minimax result obtained allows the study of a more general class of nonlinearities. It is proved the existence of solutions \((u, \lambda) \in H^1 (\mathbb{R}^n) \times \mathbb{R}\) for the equation \[ - \Delta u + pu - N(u) = \lambda u, \quad u \neq 0 \] where \(\lambda\) is located in a prescribed gap of the spectrum of \(- \Delta u + pu\), the function \(p\) is periodic and the superlinear term \(N\) derives from a potential but is not assumed to be compact.