Multiple Solutions for Schrodinger Equations Involving Concave-Convex Nonlinearities Without (AR)-Type Condition

We obtain the multiplicity of solutions for the following Schrodinger equations {-Delta u + V(x)u = g(x, u) for x is an element of R-N, u(x) -> 0 as vertical bar u vertical bar -> infinity, where V is an element of C(R-N, R) is coercive at infinity and g involves concave-convex nonlinearities while the convex terms need not to satisfy the (AR)-type condition. Some new nonlinearities are considered and an example is given.