A Nonlinear Schrödinger Equation Resonating at an Essential Spectrum
Keyword(s):
We consider the nonlinear Schrödinger equation-Δu+f(u)=V(x)u in RN. The potential functionVsatisfies that the essential spectrum of the Schrödinger operator-Δ-Vis[0,+∞)and this Schrödinger operator has infinitely many negative eigenvalues accumulating at zero. The nonlinearityfsatisfies the resonance type conditionlimt→∞f(t)/t=0. Under some additional conditions onVandf, we prove that this equation has infinitely many solutions.
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