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Ground States of Nonlinear Schrodinger-Kirchhoff Type Equation
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作者 Weidan Li 《Journal of Applied Mathematics and Physics》 2020年第2期307-314,共8页
In this paper, we considered with the following Schr&#246;dinger-Kirchhoff type problem: -(a+b?&#643;RN|&#8711;u|2dx)&#8711;u + V(x)u = f(x,u) in RN. We put forward general assumptions on the nonlinear... In this paper, we considered with the following Schr&#246;dinger-Kirchhoff type problem: -(a+b?&#643;RN|&#8711;u|2dx)&#8711;u + V(x)u = f(x,u) in RN. We put forward general assumptions on the nonlinearity f with the subcritical growth and we find a ground state solution being a minimizer of the energy functional associated with a Nehari-Pankov manifold by using a linking theorem. 展开更多
关键词 schrodinger-Kirchhoff LINKING Ceramisequence fatou’s Lemma
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Factorization of proper holomorphic maps on irreducible bounded symmetric domains of rank≥2 被引量:2
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作者 MOK Ngaiming NG Sui-Chung 《Science China Mathematics》 SCIE 2010年第3期813-826,共14页
We obtain rigidity results on arbitrary proper holomorphic maps F from an irreducible bounded symmetric domain Ω of rank ≥2 into any complex space Z. After lifting to the normalization of the subvariety F (Ω) Z, we... We obtain rigidity results on arbitrary proper holomorphic maps F from an irreducible bounded symmetric domain Ω of rank ≥2 into any complex space Z. After lifting to the normalization of the subvariety F (Ω) Z, we prove that F must be the canonical projection map to the quotient space of Ω by a finite group of automorphisms. The approach is along the line of the works of Mok and Tsai by considering radial limits of bounded holomorphic functions derived from F and proving that proper holomorphic maps between bounded symmetric domains preserve certain totally geodesic subdomains. In contrast to the previous works, in general we have to deal with multivalent holomorphic maps for which Fatou’s theorem cannot be applied directly. We bypass the difficulty by devising a limiting process for taking radial limits of correspondences arising from proper holomorphic maps and by elementary estimates allowing us to define distinct univalent branches of the underlying multivalent map on certain subsets. As a consequence of our rigidity result, with the exception of Type-IV domains, any proper holomorphic map f : Ω→ D of Ω onto a bounded convex domain D is necessarily a biholomorphism. In the exceptional case where Ω is a Type-IV domain, either f is a biholomorphism or it is a double cover branched over a totally geodesic submanifold which can be explicitly described. 展开更多
关键词 bounded symmetric domain PROPER HOLOMORPHIC map fatou’s theorem correspondence DIsCRIMINANT G-sTRUCTURE
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