On the Existence and Uniqueness of Dirichlet Problems on a Positive Half-Line
Keywords:
Global diffeomorphism, Palais-Smale, calculus of variations, boundary value prob lem, half-line.Abstract
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.
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