Compactness via monotonicity in nonsmooth critical point theory, with application to Born-Infeld type equations

Autor:	Byeon, Jaeyoung, Ikoma, Norihisa, Malchiodi, Andrea, Mari, Luciano
Rok vydání:	2024
Předmět:	Mathematics - Analysis of PDEs 35A15 58E05 58E35 35B38 35J62
Druh dokumentu:	Working Paper
Popis:	In this paper, we prove new existence and multiplicity results for critical points of lower semicontinuous functionals in Banach spaces, complementing the nonsmooth critical point theory set forth by Szulkin and avoiding the need of the Palais-Smale condition. We apply our abstract results to get entire solutions with finite energy to Born-Infeld type autonomous equations. More precisely, under almost optimal conditions on the nonlinearity, we construct a positive solution and infinitely many solutions both in the classes of radially symmetric functions and nonradiallly symmetric ones. Comment: 59 pages. Comments are welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2406.14853 Zobrazit plný text záznamu View this record from Arxiv