Interior Bubbling Solutions for an Elliptic Equation with Slightly Subcritical Nonlinearity

Khalil El Mehdi () and Fatimetou Mohamed Salem
Additional contact information
Khalil El Mehdi: Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia
Fatimetou Mohamed Salem: Faculté des Sciences et Techniques, Université de Nouakchott, Nouakchott 2373, Mauritania

Mathematics, 2023, vol. 11, issue 6, 1-28

Abstract: In this paper, we considered the Neumann elliptic equation ( P ε ) : − Δ u + K ( x ) u = u ( n + 2 ) / ( n − 2 ) − ε , u > 0 in Ω , ∂ u / ∂ ν = 0 on ∂ Ω , where Ω is a smooth bounded domain in R n , n ≥ 6 , ε is a small positive real and K is a smooth positive function on Ω ¯ . Using refined asymptotic estimates of the gradient of the associated Euler–Lagrange functional, we constructed simple and non-simple interior bubbling solutions of ( P ε ) which allowed us to prove multiplicity results for ( P ε ) provided that ε is small. The existence of non-simple interior bubbling solutions is a new phenomenon for the positive solutions of subcritical problems.

Keywords: partial differential equations; nonlinear equations; Neumann elliptic problems; critical Sobolev exponent (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/6/1471/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/6/1471/ (text/html)

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:gam:jmathe:v:11:y:2023:i:6:p:1471-:d:1100358

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().