Geodesic
Existence Theorems for the Dirichlet Elliptic Inclusion Involving Exponential-Growth-Type Multivalued Right-Hand Side
Hôǹg Thái Nguyêñ 1   ; Dariusz Pączka 2
1 Institute of Mathematics Szczecin University Wielkopolska 15 70-451 Szczecin, Poland
2 Institute of Mathematics Szczecin Technical University Al. Piastów 48/49 70-310 Szczecin, Poland
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) no. 4, pp. 361-375 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $\Omega\subset \mathbb{R}^2$. 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.
DOI : 10.4064/ba53-4-2
Keywords: present existence results dirichlet elliptic inclusion upper semicontinuous multivalued right hand side exponential type orlicz spaces involving vector laplacian subject dirichlet boundary conditions domain omega subset mathbb first result obtained via multivalued version leray schauder principle together nakano dieudonn sequential weak compactness criterion second result obtained using nonsmooth variational technique together formula clarkes subgradient lipschitz integral functionals nonregular orlicz spaces

Hôǹg Thái Nguyêñ  1   ; Dariusz Pączka  2

1 Institute of Mathematics Szczecin University Wielkopolska 15 70-451 Szczecin, Poland
2 Institute of Mathematics Szczecin Technical University Al. Piastów 48/49 70-310 Szczecin, Poland 
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     author = {H\^oǹg Th\'ai Nguy\^e\~n and Dariusz P\k{a}czka},
     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},
     pages = {361--375},
     year = {2005},
     volume = {53},
     number = {4},
     doi = {10.4064/ba53-4-2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/ba53-4-2/}
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 Multivalued Right-Hand Side
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 Involving Exponential-Growth-Type
 Multivalued Right-Hand Side
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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) no. 4, pp. 361-375. doi: 10.4064/ba53-4-2

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