The existence of minimizers of the action functional without convexity assumption

Aleksandra Orpel

DOI: http://dx.doi.org/10.12775/TMNA.2002.032

Abstract


We shall prove the existence of minimizers of the following functional $
f(u)=\int_{0}^{T}L(x,u(x),u'(x))dx$ without convexity
assumption. As a consequence of this result and the duality described in
[A. Nowakowski, < i> Metody wariacyjne dla nieliniowych problemów Dirichleta< /i> (Chapter
6), Wydawnictwo Naukowo Techniczne, Warszawa, 1994] we derive the existence of solutions for the Dirichlet problem for
a certain differential inclusion being a generalization of the
Euler-Lagrange equation of the functional $f$.

Keywords


Dirichlet problem; duality; variational principle; Euler-Lagrange equation

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