Abstract :
In this paper we study the existence of a nontrivial H2( N) solution for an equation of the form where p L∞( N) is a periodic function. We assume that the operator −Δ + p − λ : H2( N) L2( N) → L2( N) is strongly indefinite and invertible and that ƒ(x, •): → is odd and satisfies some superlinear but subcritical growth conditions. We extend the class of nonlinearities which has been studied up to now. In particular, under standard technical restrictions, the existence of a solution is derived, when limx → ∞, f(x, s) ≡ (s) > 0 exists for all s , if we assume that f(x, s) ≥ (s) for all s and a.e. on N.
