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Nonlinear unilateral problems in Orlicz spaces

L. Aharouch, E. Azroul, M. Rhoudaf (2006)

Applicationes Mathematicae

We prove the existence of solutions of the unilateral problem for equations of the type Au - divϕ(u) = μ in Orlicz spaces, where A is a Leray-Lions operator defined on ( A ) W ¹ L M ( Ω ) , μ L ¹ ( Ω ) + W - 1 E M ̅ ( Ω ) and ϕ C ( , N ) .

Nonlocal elliptic problems

Andrzej Krzywicki, Tadeusz Nadzieja (2000)

Banach Center Publications

Some conditions for the existence and uniqueness of solutions of the nonlocal elliptic problem - Δ φ = M f ( φ ) / ( ( Ω f ( φ ) ) p ) , φ | Ω = 0 are given.

Non-local Gel'fand problem in higher dimensions

Tosiya Miyasita, Takashi Suzuki (2004)

Banach Center Publications

The non-local Gel’fand problem, Δ v + λ e v / Ω e v d x = 0 with Dirichlet boundary condition, is studied on an n-dimensional bounded domain Ω. If it is star-shaped, then we have an upper bound of λ for the existence of the solution. We also have infinitely many bendings in λ of the connected component of the solution set in λ,v if Ω is a ball and 3 ≤ n ≤ 9.

Non-Newtonian fluids and function spaces

Růžička, Michael, Diening, Lars (2007)

Nonlinear Analysis, Function Spaces and Applications

In this note we give an overview of recent results in the theory of electrorheological fluids and the theory of function spaces with variable exponents. Moreover, we present a detailed and self-contained exposition of shifted N -functions that are used in the studies of generalized Newtonian fluids and problems with p -structure.

Non-topological condensates in self-dual Chern-Simons gauge theory

Takashi Suzuki, Futoshi Takahashi (2004)

Banach Center Publications

This note is concerned with the recent paper "Non-topological N-vortex condensates for the self-dual Chern-Simons theory" by M. Nolasco. Modifying her arguments and statements, we show that the existence of "non-topological" multi-vortex condensates follows when the number of prescribed vortex points is greater than or equal to 2.

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