Bifurcation from infinity for elliptic problems on RN

被引：0

作者：

Cwiszewski, Aleksander ^{[1
]}

Kryszewski, Wojciech ^{[2
]}

机构：

[1] Nicolaus Copernicus Univ, Fac Math & Comp Sci, Torun, Poland

[2] Lodz Univ Technol, Inst Math, Lodz, Poland

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2019年 / 58卷 / 01期

关键词：

ASYMPTOTIC BIFURCATION; EQUATIONS; CONTINUATION; RESONANCE; DYNAMICS; THEOREM; INDEX;

D O I：

10.1007/s00526-018-1455-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the paper the asymptotic bifurcation of solutions to a parameterized stationary semilinear Schrodinger 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 Schrodinger 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.

引用

页数：23

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