Existence theorems for the Dirichlet elliptic inclusion involving exponential-growth-type multivalued right-hand side

• Autorzy: Nguyêñ, H. T. , Pączka, D.
• Języki publikacji: EN

Abstrakty

EN

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

EN

Dirichlet elliptic inclusion; exponential-growth-type multivalued right-hand side; weak solutions in Orlicz spaces; topological and non-smooth variational techniques; generalized gradient; subgradient in Clarke's sense; Lipschitz integral functional

• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2005
• Tom: Vol. 53, no 4
• Strony: 361-375
• Opis fizyczny: Bibliogr. 34 poz.

Twórcy

autor

Nguyêñ, H. T.

• Institute of Mathematics, Szczecin University, Wielkopolska 15, 70-451 Szczecin, Poland,

autor

Pączka, D.

• Institute of Mathematics, Szczecin Technical University, Al. Piastów 48/49, 70-310 Szczecin, Poland,

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Identyfikatory

DOI

10.4064/ba53-4-2