Blow-up solutions for Hardy–Sobolev equations on compact Riemannian manifolds

2018 ◽  
Vol 20 (3) ◽  
Author(s):  
Wenjing Chen
Keyword(s):  
Riemannian Manifolds ◽  
Blow Up ◽  
Sobolev Equations

Blow-up solutions for asymptotically critical elliptic equations on Riemannian manifolds

2009 ◽  
Vol 58 (4) ◽  
pp. 1719-1746 ◽  
Author(s):  
Anna Maria Micheletti ◽  
Angela Pistoia ◽  
Jerome Vetois
Keyword(s):  
Riemannian Manifolds ◽  
Elliptic Equations ◽  
Blow Up

scholarly journals Clustered solutions for supercritical elliptic equations on Riemannian manifolds

2018 ◽  
Vol 8 (1) ◽  
pp. 1213-1226 ◽  
Author(s):  
Wenjing Chen
Keyword(s):  
Riemannian Manifold ◽  
Positive Integer ◽  
Riemannian Manifolds ◽  
Elliptic Problem ◽  
Elliptic Equations ◽  
Compact Riemannian Manifold ◽  
Blow Up ◽  
Beltrami Operator ◽  
Real Parameter ◽  
Reduction Procedure

Abstract Let {(M,g)} be a smooth compact Riemannian manifold of dimension {n\geq 5} . We are concerned with the following elliptic problem: -\Delta_{g}u+a(x)u=u^{\frac{n+2}{n-2}+\varepsilon},\quad u>0\text{ in }M, where {\Delta_{g}=\mathrm{div}_{g}(\nabla)} is the Laplace–Beltrami operator on M, {a(x)} is a {C^{2}} function on M such that the operator {-\Delta_{g}+a} is coercive, and {\varepsilon>0} is a small real parameter. Using the Lyapunov–Schmidt reduction procedure, we obtain that the problem under consideration has a k-peaks solution for positive integer {k\geq 2} , which blow up and concentrate at one point in M.

Positive solutions for a quasilinear system Via blow up

1993 ◽  
Vol 18 (12) ◽  
pp. 2071-2106
Author(s):  
Philippe Clément ◽  
Raúl Manásevich ◽  
Enzo Mitidieri
Keyword(s):  
Positive Solutions ◽  
Blow Up ◽  
Quasilinear System

: The Blow-Up . Michelangelo Antonioni .

1967 ◽  
Vol 20 (3) ◽  
pp. 28-31
Author(s):  
Max Kozloff
Keyword(s):  
Blow Up ◽  
Michelangelo Antonioni
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