This paper deals with existence and multiplicity of positive solutions for the equation -Delta u + epsilon u = u n+2/n-2 epsilon > 0, with zero Dirichlet boundary condition in bounded domains. For large k and small epsilon, the existence of k-spike solutions is proved under suitable assumptions on the shape of the domain. In particular, domains that are arbitrarily close to starshaped domains are allowed (no positive solution there exists if the domain is starshaped).
Molle, R., Passaseo, D. (2007). Multispike solutions of nonlinear elliptic equations with critical Sobolev exponent. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 32(4-6), 797-818 [10.1080/03605300600781642].
Multispike solutions of nonlinear elliptic equations with critical Sobolev exponent
MOLLE, RICCARDO;
2007-01-01
Abstract
This paper deals with existence and multiplicity of positive solutions for the equation -Delta u + epsilon u = u n+2/n-2 epsilon > 0, with zero Dirichlet boundary condition in bounded domains. For large k and small epsilon, the existence of k-spike solutions is proved under suitable assumptions on the shape of the domain. In particular, domains that are arbitrarily close to starshaped domains are allowed (no positive solution there exists if the domain is starshaped).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
