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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
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