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/