We discuss the existence of solutions for a certain generalization of the membrane equation and their continuous dependence on function parameters. We apply variational methods and consider the PDE as the Euler-Lagrange equation for a certain integral functional, which is not necessarily convex and coercive. As a consequence of the duality theory we obtain variational principles for our problem and some numerical results concerning approximation of solutions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-1-14,
author = {Aleksandra Orpel},
title = {Continuous dependence on function parameters for superlinear Dirichlet problems},
journal = {Colloquium Mathematicae},
volume = {103},
year = {2005},
pages = {131-148},
zbl = {1273.35111},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-1-14}
}
Aleksandra Orpel. Continuous dependence on function parameters for superlinear Dirichlet problems. Colloquium Mathematicae, Tome 103 (2005) pp. 131-148. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-1-14/