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Abstrakty
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.
Słowa kluczowe
Kategorie tematyczne
- 47H30: Particular nonlinear operators (superposition, Hammerstein, Nemytski{\u\i}, Uryson, etc.)
- 35R70: Partial differential equations with multivalued right-hand sides
- 47H04: Set-valued operators
- 54C60: Set-valued maps
- 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
- 49J53: Set-valued and variational analysis
- 49J52: Nonsmooth analysis
Rocznik
Tom
Numer
Strony
361-375
Opis fizyczny
Daty
wydano
2005
Twórcy
autor
- Institute of Mathematics, Szczecin University, Wielkopolska 15, 70-451 Szczecin, Poland
autor
- Institute of Mathematics, Szczecin Technical University, Al. Piastów 48/49, 70-310 Szczecin, Poland
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
DOI
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-4-2