The existence of minimizers of the action functional without convexity assumption
Keywords
Dirichlet problem, duality, variational principle, Euler-Lagrange equationAbstract
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 $f$.Downloads
Published
2002-09-01
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1.
ORPEL, Aleksandra. The existence of minimizers of the action functional without convexity assumption. Topological Methods in Nonlinear Analysis. Online. 1 September 2002. Vol. 20, no. 1, pp. 179 - 193. [Accessed 19 April 2024].
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