Uniqueness Results and Asymptotic Behaviour of Nonlinear Schrödinger–Kirchhoff Equations

In this paper, we first study the uniqueness and symmetry of solution of nonlinear Schrödinger–Kirchhoff equations with constant coefficients. Then, we show the uniqueness of the solution of nonlinear Schrödinger–Kirchhoff equations with the polynomial potential. In the end, we investigate the asymp...

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Bibliographic Details
Published inSymmetry (Basel) Vol. 15; no. 10; p. 1856
Main Author Sun, Dongdong
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.10.2023
Subjects
asymptotic behaviour
Asymptotic properties
Energy
Energy industry
Kirchhoff, Gustav Robert
Mathematical analysis
Polynomials
Schrodinger equation
Schrödinger–Kirchhoff equations
symmetry
Uniqueness
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Summary:In this paper, we first study the uniqueness and symmetry of solution of nonlinear Schrödinger–Kirchhoff equations with constant coefficients. Then, we show the uniqueness of the solution of nonlinear Schrödinger–Kirchhoff equations with the polynomial potential. In the end, we investigate the asymptotic behaviour of the positive least energy solutions to nonlinear Schrödinger–Kirchhoff equations with vanishing potentials. The vanishing potential means that the zero set of the potential is non-empty. The uniqueness results of Schrödinger equations and the scaling technique are used in our proof. The elliptic estimates and energy analysis are applied in the proof of the asymptotic behaviour of the above Schrödinger–Kirchhoff-type equations.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym15101856