Minimax Theory and its Applications 04 (2019), No. 1, 055--069
Copyright Heldermann Verlag 2019
On the Existence and Uniqueness of Dirichlet Problems on a Positive Half-Line
Michal Beldzinski
Institute of Mathematics, Lodz University of Technology, Wolczanska 215, 90-924 Lodz, Poland
beldzinski.michal@outlook.com
Marek Galewski
Institute of Mathematics, Lodz University of Technology, Wolczanska 215, 90-924 Lodz, Poland
marek.galewski@p.lodz.pl
We consider Dirichlet problems on a positive half-line. The methods which we apply and compare are the usage of a global invertibility theorem and of a direct variational approach. For both approaches the solution is the limit of a strongly convergent minimizing sequence to a suitably chosen action functional. Moreover, we show that the Euler action functional satisfies the PS condition at the infimal level.
Keywords: Global diffeomorphism, Palais-Smale, calculus of variations, boundary value problem, half-line.
MSC: 34B15, 46T20, 49Q99.
[ Fulltext-pdf (116 KB)] for subscribers only.