Existence Theorems for the Dirichlet Elliptic Inclusion Involving Exponential-Growth-Type Multivalued Right-Hand Side

• Autorzy: Hôǹg Thái Nguyêñ , Dariusz Pączka
• 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.

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2005
• Tom: 53
• Numer: 4
• Strony: 361-375

Daty

wydano

2005

Twórcy

autor

Hôǹg Thái Nguyêñ

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

autor

Dariusz Pączka

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

Identyfikatory

DOI

10.4064/ba53-4-2