## Lower bounds for the counting function of resonances for a perturbation of a periodic Schrödinger operator by decreasing potential.(English)Zbl 1032.35063

Summary: We are interested here in the counting function of resonances $$N(h)$$ for a perturbation of a periodic Schrödinger operator $$P_0$$ by decreasing potential $$W(hx)$$ $$(h\searrow 0)$$. We obtain a lower bound for $$N(h)$$ near some singularities of the density of states measure, associated to the unperturbed Hamiltonian $$P_0$$.

### MSC:

 35J10 Schrödinger operator, Schrödinger equation 35B34 Resonance in context of PDEs 35B20 Perturbations in context of PDEs

### Keywords:

edges of bands; band crossing
Full Text:

### References:

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