Nodal solution for critical Kirchhoff-type equation with fast increasing weight in R2

In this paper, we investigate the existence of a least-energy sign-changing solutions for the following Kirchhoff-type equation: − ( 1 + b ∫ R 2 K ( x ) | ∇ u | 2 d x ) div ( K ( x ) ∇ u ) = K ( x ) f ( u ) , x ∈ R 2 , where f has exponential subcritical or exponential critical growth in the sense o...

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Bibliographic Details
Published in:Journal of inequalities and applications 2023-03, Vol.2023 (1), p.40
Main Authors: Qin, Qin, Jie, Guo, Suo, Hongmin
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Existence theorems
Inequality
Mathematics
Mathematics and Statistics
Variational methods
Online Access:Get full text
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Summary:In this paper, we investigate the existence of a least-energy sign-changing solutions for the following Kirchhoff-type equation: − ( 1 + b ∫ R 2 K ( x ) | ∇ u | 2 d x ) div ( K ( x ) ∇ u ) = K ( x ) f ( u ) , x ∈ R 2 , where f has exponential subcritical or exponential critical growth in the sense of the Trudinger–Moser inequality. By using the constrained variational methods, combining the deformation lemma and Miranda’s theorem, we prove the existence of a least-energy sign-changing solution. Moreover, we also prove that this sign-changing solution has exactly two nodal domains.
ISSN:1025-5834
1029-242X
DOI:10.1186/s13660-023-02945-x