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The discrete spectrum in gaps of the perturbed periodic Schrödinger operator. I: Regular perturbations. (English) Zbl 0848.47032
Demuth, Michael (ed.) et al., Boundary value problems, Schrödinger operators, deformation quantization. Berlin: Akademie Verlag. Math. Top. 8, 334-352 (1995).
Let $$A=- \text{div} (g(x) \text{grad})+ p(x)$$ be an elliptic periodic operator in $$L^2 (\mathbb{R}^d)$$, $$d>2$$; $$\Lambda= (\lambda_-, \lambda_+)$$ is a gap in the spectrum of $$A$$; $$A_+ (\alpha)= A- \alpha V$$, $$0\leq V\in L^{d/2} (\mathbb{R}^d)$$. The author investigates asymptotics of the number of eigenvalues of $$A_+ (t)$$, appearing in the point $$\lambda_+$$ as $$t$$ increased from zero to $$\alpha$$.
For the entire collection see [Zbl 0830.00010].

##### MSC:
 47F05 General theory of partial differential operators (should also be assigned at least one other classification number in Section 47-XX) 35P20 Asymptotic distributions of eigenvalues in context of PDEs 47A55 Perturbation theory of linear operators