Solutions concentrating on higher dimensional subsets for singularly perturbed elliptic equations I

• Autores: Thomas Bartsch, Shuangjie Peng
• Localización: Indiana university mathematics journal, ISSN 0022-2518, Vol. 57, Nº 4, 2008, págs. 1599-1632
• Idioma: inglés
• DOI: 10.1512/iumj.2008.57.3243
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• Resumen

  • We consider the singularly perturbed equation -e2?u+V(x)u=K(x)up-1 on a domain O?RN which may be bounded or unbounded. Under suitable hypotheses on V , K we construct layered solutions u?H01(O) which concentrate on certain high-dimensional subsets of O . This gives a positive answer to a problem proposed by Ambrosetti, Malchiodi and Ni in [1].