Barrier Solutions of Elliptic Differential Equations in Musielak-Orlicz-Sobolev Spaces
In this paper, we study the solution set of the following Dirichlet boundary equation: −diva1x,u,Du+a0x,u=fx,u,Du in Musielak-Orlicz-Sobolev spaces, where a1:Ω×ℝ×ℝN⟶ℝN, a0:Ω×ℝ⟶ℝ, and f:Ω×ℝ×ℝN⟶ℝ are all Carathéodory functions. Both a1 and f depend on the solution u and its gradient Du. By using a lin...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/9927898 |
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| Summary: | In this paper, we study the solution set of the following Dirichlet boundary equation: −diva1x,u,Du+a0x,u=fx,u,Du in Musielak-Orlicz-Sobolev spaces, where a1:Ω×ℝ×ℝN⟶ℝN, a0:Ω×ℝ⟶ℝ, and f:Ω×ℝ×ℝN⟶ℝ are all Carathéodory functions. Both a1 and f depend on the solution u and its gradient Du. 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. |
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| ISSN: | 2314-8896 2314-8888 |