Multiplicity of solutions of asymptotically linear Dirichlet problems associated to second order equations in $\mathbb R^{2n+1}$

Abstract

We present a result about multiplicity of solutions of asymptotically linear Dirichlet problems associated to second order equations in $\mathbb R^{2n+1}$, $n \ge 1$. Under an additional technical condition, the number of solutions obtained is given by the gap between the Morse indexes of the linearizations at zero and infinity. The additional condition is stable with respect to small perturbations of the vector field. We show with a simple example that in some cases the size of the perturbation can be explicitly estimated.