Bifurcation from infinity for elliptic problems on R^N

2018/06/08 by Aleksander Ćwiszewski, Ćwiszewski, Aleksander, Wojciech Kryszewski +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1806.03312

arxiv created 2018/06/08 · openalex publication_date 2018/06/08 · arxiv updated 2018/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the paper the asymptotic bifurcation of solutions to a parameterized stationary semilinear Schrödinger equation involving a potential of the Kato-Rellich type is studied. It is shown that the bifurcation from infinity occurs if the parameter is an eigenvalue of the hamiltonian lying below the asymptotic bottom of the bounded part of the potential. Thus the bifurcating solution are related to bound states of the corresponding Schrödinger equation. The argument relies on the use of the (generalized) Conley index due to Rybakowski and resonance assumptions of the Landesman-Lazer or sign-condition type.

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