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/