[Solutions positives pour l'équation Δu+u(n+2)/(n−2)+ε=0 en ouverts contractibles]
On donne des exemples d'ouverts bornés , même contractibles, satisfaisant la propriété suivante : il existe tel que, pour tout , le problème ci-dessous, pour ε>0 suffisamment petit, a des solutions qui pour ε→0 explosent exactement en k points. On prouve aussi que ces points convergent vers des points de quand k→∞.
We give examples of bounded domains , even contractible, having the following property: there exists such that, for every integer , problem below, for ε>0 small enough, has at least one solution blowing up as ε→0 at exactly k points. We also prove that the blow-up points tend to some points of as k→∞.
Publié le :
Riccardo Molle 1 ; Donato Passaseo 2
@article{CRMATH_2002__335_5_459_0, author = {Riccardo Molle and Donato Passaseo}, title = {Positive solutions for slightly super-critical elliptic equations in contractible domains}, journal = {Comptes Rendus. Math\'ematique}, pages = {459--462}, publisher = {Elsevier}, volume = {335}, number = {5}, year = {2002}, doi = {10.1016/S1631-073X(02)02502-5}, language = {en}, }
TY - JOUR AU - Riccardo Molle AU - Donato Passaseo TI - Positive solutions for slightly super-critical elliptic equations in contractible domains JO - Comptes Rendus. Mathématique PY - 2002 SP - 459 EP - 462 VL - 335 IS - 5 PB - Elsevier DO - 10.1016/S1631-073X(02)02502-5 LA - en ID - CRMATH_2002__335_5_459_0 ER -
Riccardo Molle; Donato Passaseo. Positive solutions for slightly super-critical elliptic equations in contractible domains. Comptes Rendus. Mathématique, Volume 335 (2002) no. 5, pp. 459-462. doi : 10.1016/S1631-073X(02)02502-5. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02502-5/
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