We deal with the existence of solutions of the Dirichlet problem for sublinear and superlinear partial differential inclusions considered as generalizations of the Euler-Lagrange equation for a certain integral functional without convexity assumption. We develop a duality theory and variational principles for this problem. As a consequence of the duality theory we give a numerical version of the variational principles which enables approximation of the solution for our problem.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap85-3-1,
author = {Aleksandra Orpel},
title = {Dirichlet problems without convexity assumption},
journal = {Annales Polonici Mathematici},
volume = {85},
year = {2005},
pages = {193-210},
zbl = {1161.35357},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap85-3-1}
}
Aleksandra Orpel. Dirichlet problems without convexity assumption. Annales Polonici Mathematici, Tome 85 (2005) pp. 193-210. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap85-3-1/