the sub-supersolution method and extremal solutions of quasilinear elliptic equations in orlicz-sobolev spaces
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2018
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Abstract
We prove the existence of extremal solutions of the following quasilinear elliptic problem -∑i=1N∂/∂xiai(x,u(x),Du(x))+g(x,u(x),Du(x))=0 under Dirichlet boundary condition in Orlicz-Sobolev spaces W01LM(Ω) and give the enclosure of solutions. The differential part is driven by a Leray-Lions operator in Orlicz-Sobolev spaces, while the nonlinear term g:Ω×R×RN→R is a Carathéodory function satisfying a growth condition. Our approach relies on the method of linear functional analysis theory and the sub-supersolution method.
| Reference Key |
dong2018journalthe
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|---|---|
| Authors | ;Ge Dong;Xiaochun Fang |
| Journal | Biosensors |
| Year | 2018 |
| DOI |
10.1155/2018/8104901
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