Normalized solutions of Kirchhoff equations with critical and subcritical nonlinearities: the defocusing case

Paulo C. Carrião (), Olímpio H. Miyagaki () and André Vicente ()
Additional contact information
Paulo C. Carrião: Universidade Federal de Minas Gerais
Olímpio H. Miyagaki: Universidade Federal de São Carlos
André Vicente: Universidade Estadual do Oeste do Paraná

Partial Differential Equations and Applications, 2022, vol. 3, issue 5, 1-16

Abstract: Abstract In this paper, we study the following problem $$\begin{aligned} -\left( a + b\int _{{\mathbb {R}}^3}\arrowvert \nabla u\arrowvert ^2 \right) \Delta u =\lambda u +\arrowvert u\arrowvert ^{p-2}u+\mu \arrowvert u\arrowvert ^{q-2}u \,\,\text{ in } {\mathbb {R}}^3, \end{aligned}$$ - a + b ∫ R 3 | ∇ u | 2 Δ u = λ u + | u | p - 2 u + μ | u | q - 2 u in R 3 , under the constraint $$\int _{{\mathbb {R}}^3}u^2=c^2$$ ∫ R 3 u 2 = c 2 , where a, b, and c are positive constants, $$\lambda $$ λ is a real number, $$\mu

Keywords: Kirchhoff equation; Defocusing case; Normalized solutions; Critical exponents; 35A15; 35B33; 35B38; 35J60 (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s42985-022-00201-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:pardea:v:3:y:2022:i:5:d:10.1007_s42985-022-00201-3

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/42985/

DOI: 10.1007/s42985-022-00201-3

Access Statistics for this article

Partial Differential Equations and Applications is currently edited by Zhitao Zhang

More articles in Partial Differential Equations and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().