کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4609686 | 1338523 | 2016 | 46 صفحه PDF | دانلود رایگان |
A complete analysis of the essential spectrum of matrix-differential operators AA of the formequation(0.1)(−ddtpddt+q−ddtb⁎+c⁎bddt+cD)in L2((α,β))⊕(L2((α,β)))n singular at β∈R∪{∞}β∈R∪{∞} is given; the coefficient functions p, q are scalar real-valued with p>0p>0, b, c are vector-valued, and D is Hermitian matrix-valued. The so-called “singular part of the essential spectrum” σesss(A) is investigated systematically. Our main results include an explicit description of σesss(A), criteria for its absence and presence; an analysis of its topological structure and of the essential spectral radius. Our key tools are: the asymptotics of the leading coefficient π(⋅,λ)=p−b⁎(D−λ)−1bπ(⋅,λ)=p−b⁎(D−λ)−1b of the first Schur complement of (0.1), a scalar differential operator but non-linear in λ; the Nevanlinna behaviour in λ of certain limits t↗βt↗β of functions formed out of the coefficients in (0.1). The efficacy of our results is demonstrated by several applications; in particular, we prove a conjecture on the essential spectrum of some symmetric stellar equilibrium models.
Journal: Journal of Differential Equations - Volume 260, Issue 4, 15 February 2016, Pages 3881–3926