On the compactness of the resolvent of a Schrödinger type singular operator with a negative parameter

Mussakan B. Muratbekov and Madi M. Muratbekov

Chaos, Solitons & Fractals, 2021, vol. 151, issue C

Abstract: In this paper, we consider a Schrödinger-type operator with a negative parameter and a complex potential Lt=−Δ+(−t2+itb(x)+q(x)),x∈Rn,n≥1,i2=−1, where t is a parameter that arises when studying hyperbolic operators in the space L2(Rn+1). We assume with respect to the coefficients of the operator Lt that they are continuous in Rn strongly growing and rapidly oscillating functions at infinity and satisfy the condition |b(x)|≥δ0>0,q(x)≥δ>0.

Keywords: Schrödinger operator; Singular differential operator; Hyperbolic type; Negative parameter; Coercive estimates; Compactness of the resolvent (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:151:y:2021:i:c:s0960077921006020

DOI: 10.1016/j.chaos.2021.111248

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