Bound states for semilinear Schrodinger equations with sign-changing potential

We study the existence and the number of decaying solutions for the semilinear Schrodinger equations - epsilon(2)Delta u + V( x) u = g( x, u), epsilon > 0 small, and - Delta u + lambda V(x) u = g( x, u) lambda > 0 large. The potential V may change sign and g is either asymptotically linear or superlinear ( but subcritical) in u as vertical bar u vertical bar -> infinity.