Some existence results for superlinear elliptic boundary value problems involving critical exponents

The existence of solutions to the problem −Δu − λu = u¦u¦ 2∗ − 2 in Ω u¦ ∂Ω = 0 is studied. For an arbitrary domain Ω ⊂ R n , if λ ϵ ]0, λ 1[ and n ⩾ 6, the existence of solutions of changing sign is obtained. If Ω = B R (0) ⊂ R n , λ ϵ ]0, λ 1[, and n ⩾ 7, infinitely many radial solutions to this p...

Full description

Saved in:
Bibliographic Details
Published inJournal of functional analysis Vol. 69; no. 3; pp. 289 - 306
Main Authors Cerami, G, Solimini, S, Struwe, M
Format Journal Article
LanguageEnglish
Published Orlando, FL Elsevier Inc 01.12.1986
San Diego, CA Academic Press
Brugge
Subjects
Exact sciences and technology
Function theory, analysis
Mathematical methods in physics
Physics
Non linear equation
Elliptic equation
Boundary value problem
Existence theorem
Partial differential equation
Solution
Online AccessGet full text

Cover

More Information
Summary:The existence of solutions to the problem −Δu − λu = u¦u¦ 2∗ − 2 in Ω u¦ ∂Ω = 0 is studied. For an arbitrary domain Ω ⊂ R n , if λ ϵ ]0, λ 1[ and n ⩾ 6, the existence of solutions of changing sign is obtained. If Ω = B R (0) ⊂ R n , λ ϵ ]0, λ 1[, and n ⩾ 7, infinitely many radial solutions to this problem are exhibited, characterized by the number of nodes they possess.
ISSN:0022-1236
1096-0783
DOI:10.1016/0022-1236(86)90094-7