We present two existence results for the Dirichlet elliptic inclusion with an upper semicontinuous multivalued right-hand side in exponential-type Orlicz spaces involving a vector Laplacian, subject to Dirichlet boundary conditions on a domain Ω⊂ ℝ². The first result is obtained via the multivalued version of the Leray-Schauder principle together with the Nakano-Dieudonné sequential weak compactness criterion. The second result is obtained by using the nonsmooth variational technique together with a formula for Clarke's subgradient for Lipschitz integral functionals on "nonregular" Orlicz spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-4-2,
author = {Hong Thai Nguyen and Dariusz Paczka},
title = {Existence Theorems for the Dirichlet Elliptic Inclusion Involving Exponential-Growth-Type Multivalued Right-Hand Side},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {53},
year = {2005},
pages = {361-375},
zbl = {1111.35140},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-4-2}
}
Hôǹg Thái Nguyêñ; Dariusz Pączka. Existence Theorems for the Dirichlet Elliptic Inclusion Involving Exponential-Growth-Type Multivalued Right-Hand Side. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) pp. 361-375. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-4-2/