Some Existence Results of Solutions for the Semilinear Elliptic Equations on N

In this paper we prove existence of W1, 2( N) solutions for the following equations on N, −Δu+q(x)u−λu=g(x, u), where the operator −Δ+q(x)−λ is indefinite, and g(x, z) is superlinear or asymptotically linear as z→∞.