We investigate the existence of solutions for the Dirichlet problem including the generalized balance of a membrane equation. We present a duality theory and variational principle for this problem. As one of the consequences of the duality we obtain some numerical results which give a measure of a duality gap between the primal and dual functional for approximate solutions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc66-0-17, author = {Aleksandra Orpel}, title = {On the existence of multiple positive solutions for a certain class of elliptic problems}, journal = {Banach Center Publications}, volume = {65}, year = {2004}, pages = {251-262}, zbl = {1235.35095}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc66-0-17} }
Aleksandra Orpel. On the existence of multiple positive solutions for a certain class of elliptic problems. Banach Center Publications, Tome 65 (2004) pp. 251-262. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc66-0-17/