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The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand.
Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.
Authors: Selim, Salem | Yan, Lili
Article Type: Research Article
Abstract: We study inverse boundary problems for the magnetic Schrödinger operator with Hölder continuous magnetic potentials and continuous electric potentials on a conformally transversally anisotropic Riemannian manifold of dimension n ⩾ 3 with connected boundary. A global uniqueness result is established for magnetic fields and electric potentials from the partial Cauchy data on the boundary of the manifold provided that the geodesic X-ray transform on the transversal manifold is injective.
Keywords: Inverse problems, magnetic Schrödinger operator, partial data, CTA manifold
DOI: 10.3233/ASY-241909
Citation: Asymptotic Analysis, vol. Pre-press, no. Pre-press, pp. 1-12, 2024
Authors: Fang, Xiang-Dong | Han, Zhi-Qing
Article Type: Research Article
Abstract: In this paper we consider the generalized quasilinear Schrödinger equations − div ( g 2 ( u ) ∇ u ) + g ( u ) g ′ ( u ) | ∇ u | 2 + V ( x ) u = h ( x , u ) , x ∈ R N , where V and h are periodic in x i , 1 ⩽ i ⩽ N …. By using variational methods, we prove the existence of ground state solutions, i.e., nontrivial solutions with least possible energy. Show more
Keywords: Quasilinear Schrödinger equation, ground state solution, asymptotically linear, Nehari manifold
DOI: 10.3233/ASY-241913
Citation: Asymptotic Analysis, vol. Pre-press, no. Pre-press, pp. 1-14, 2024
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