EconPapers    
Economics at your fingertips  
 

Sign-changing solutions for a perturbed biharmonic equation with critical exponent

Rabeh Ghoudi () and Moufida Lahrach ()
Additional contact information
Rabeh Ghoudi: University of Gabes
Moufida Lahrach: University of Gabes

Partial Differential Equations and Applications, 2025, vol. 6, issue 6, 1-21

Abstract: Abstract This paper is concerned with the following nonlinear elliptic problem with critical exponent $$(P_\varepsilon )$$ ( P ε ) : $$\Delta ^{2} u= (1+\varepsilon K(x))|u|^{(8/(n-4))}u$$ Δ 2 u = ( 1 + ε K ( x ) ) | u | ( 8 / ( n - 4 ) ) u in $$ \Omega $$ Ω , $$\Delta u=u= 0$$ Δ u = u = 0 on $$\partial \Omega $$ ∂ Ω , where $$\Omega $$ Ω is a bounded smooth domain in $$\mathbb {R}^n$$ R n , $$n\ge 5$$ n ≥ 5 , $$\varepsilon $$ ε is a small positive parameter. We prove the existence of sign-changing solution in higher dimensions: to this aim we develop a general finite-dimensional reduction procedure for perturbed variational functionals.

Keywords: Biharmonic equation; Critical Sobolev exponent; Finite-dimensional reduction; Sign-changing solutions; 35J20; 35J60 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s42985-025-00355-w 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:6:y:2025:i:6:d:10.1007_s42985-025-00355-w

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

DOI: 10.1007/s42985-025-00355-w

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 ().

 
Page updated 2025-10-12
Handle: RePEc:spr:pardea:v:6:y:2025:i:6:d:10.1007_s42985-025-00355-w