Solutions of Semilinear Elliptic Equations With Many Isolated Singularities: The Unstable Case.

Given n distinct points x 1 ; : : : ; x n in R 3 (n 2 N; n 2), we prove the existence of\Omega a regular connected open domain of R 3 containing \Sigma = fx 1 ; : : : ; x n g and the existence of a positive weak solution of \Deltau + e u = 0 in\Omega ; with nonremovable singularities at x i for every 1 i n. R'esum'e ' Etant donn'es n points distincts x 1 ; : : : ; x n de R 3 (n 2 N; n 2), on d'emontre l'existence d'un ouvert r'egulier connexe\Omega de R 3 , contenant \Sigma = fx 1 ; : : : ; x n g et l'existence d'une solution faible, positive de \Deltau + e u = 0 dans\Omega ; qui est singuli`ere en tout point de \Sigma. 1 Introduction The study of the problem \Deltau + e u = 0; (1) where the function u is defined in some domain of a R N (N 3) and where the constant ? 0, has interested many authors since 1897. V. R. Emden [4] was the first of them and his studies were motivated by the possible physical applications. Later, this problem draw the attention o..

Partial differential equations arising from physics and geometry: a volume in memory of Abbas Bahri

Presents the state of the art in PDEs, including the latest research and short courses accessible to graduate students

Partial Differential Equations Arising from Physics and Geometry

International audienc