
Minimax Theory and its Applications 04 (2019), No. 1, 055069 Copyright Heldermann Verlag 2019 On the Existence and Uniqueness of Dirichlet Problems on a Positive HalfLine Michal Beldzinski Institute of Mathematics, Lodz University of Technology, Wolczanska 215, 90924 Lodz, Poland beldzinski.michal@outlook.com Marek Galewski Institute of Mathematics, Lodz University of Technology, Wolczanska 215, 90924 Lodz, Poland marek.galewski@p.lodz.pl We consider Dirichlet problems on a positive halfline. 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, PalaisSmale, calculus of variations, boundary value problem, halfline. MSC: 34B15, 46T20, 49Q99. [ Fulltextpdf (116 KB)] for subscribers only. 