Barrier Solutions of Elliptic Differential Equations in Musielak-Orlicz-Sobolev Spaces
Keyword(s):
In this paper, we study the solution set of the following Dirichlet boundary equation: − div a 1 x , u , D u + a 0 x , u = f x , u , D u in Musielak-Orlicz-Sobolev spaces, where a 1 : Ω × ℝ × ℝ N ⟶ ℝ N , a 0 : Ω × ℝ ⟶ ℝ , and f : Ω × ℝ × ℝ N ⟶ ℝ are all Carathéodory functions. Both a 1 and f depend on the solution u and its gradient D u . By using a linear functional analysis method, we provide sufficient conditions which ensure that the solution set of the equation is nonempty, and it possesses a greatest element and a smallest element with respect to the ordering “≤,” which are called barrier solutions.
2018 ◽
Vol 2018
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pp. 1-6
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1990 ◽
Vol 148
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pp. 263-273
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1979 ◽
Vol 34
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pp. 14-23
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2000 ◽
Vol 130
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pp. 877-908
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