Existence and multiplicity of solutions for a degenerate nonlocal elliptic differential equation
Using variational arguments, we study the existence and multiplicity of solutions for the degenerate nonlocal differential equation $$displaylines{ - MBig(int_Omega |x|^{-ap}|abla u|^p,dxBig)operatorname{div} Big(|x|^{-ap}|abla u|^{p-2}abla uBig) = |x|^{-p(a+1)+c} f(x,u) quad hbox{in } Omega,cr...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2013-06-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2013/148/abstr.html |
| _version_ | 1818760326294798336 |
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| author | Nguyen Thanh Chung Hoang Quoc Toan |
| author_facet | Nguyen Thanh Chung Hoang Quoc Toan |
| author_sort | Nguyen Thanh Chung |
| collection | DOAJ |
| description | Using variational arguments, we study the existence and multiplicity of solutions for the degenerate nonlocal differential equation $$displaylines{ - MBig(int_Omega |x|^{-ap}|abla u|^p,dxBig)operatorname{div} Big(|x|^{-ap}|abla u|^{p-2}abla uBig) = |x|^{-p(a+1)+c} f(x,u) quad hbox{in } Omega,cr u = 0 quad hbox{on } partialOmega, }$$ where $Omega subset mathbb{R}^N$ ($N geq 3$) and the function M may be zero at zero. |
| first_indexed | 2024-12-18T06:56:50Z |
| format | Article |
| id | doaj.art-16c798a953fd4e0daf11de0bc7a4c787 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-18T06:56:50Z |
| publishDate | 2013-06-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-16c798a953fd4e0daf11de0bc7a4c7872022-12-21T21:17:09ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912013-06-012013148,113Existence and multiplicity of solutions for a degenerate nonlocal elliptic differential equationNguyen Thanh ChungHoang Quoc ToanUsing variational arguments, we study the existence and multiplicity of solutions for the degenerate nonlocal differential equation $$displaylines{ - MBig(int_Omega |x|^{-ap}|abla u|^p,dxBig)operatorname{div} Big(|x|^{-ap}|abla u|^{p-2}abla uBig) = |x|^{-p(a+1)+c} f(x,u) quad hbox{in } Omega,cr u = 0 quad hbox{on } partialOmega, }$$ where $Omega subset mathbb{R}^N$ ($N geq 3$) and the function M may be zero at zero.http://ejde.math.txstate.edu/Volumes/2013/148/abstr.htmlDegenerate nonlocal problemsexistence o solutionsmultiplicityvariational methods |
| spellingShingle | Nguyen Thanh Chung Hoang Quoc Toan Existence and multiplicity of solutions for a degenerate nonlocal elliptic differential equation Electronic Journal of Differential Equations Degenerate nonlocal problems existence o solutions multiplicity variational methods |
| title | Existence and multiplicity of solutions for a degenerate nonlocal elliptic differential equation |
| title_full | Existence and multiplicity of solutions for a degenerate nonlocal elliptic differential equation |
| title_fullStr | Existence and multiplicity of solutions for a degenerate nonlocal elliptic differential equation |
| title_full_unstemmed | Existence and multiplicity of solutions for a degenerate nonlocal elliptic differential equation |
| title_short | Existence and multiplicity of solutions for a degenerate nonlocal elliptic differential equation |
| title_sort | existence and multiplicity of solutions for a degenerate nonlocal elliptic differential equation |
| topic | Degenerate nonlocal problems existence o solutions multiplicity variational methods |
| url | http://ejde.math.txstate.edu/Volumes/2013/148/abstr.html |
| work_keys_str_mv | AT nguyenthanhchung existenceandmultiplicityofsolutionsforadegeneratenonlocalellipticdifferentialequation AT hoangquoctoan existenceandmultiplicityofsolutionsforadegeneratenonlocalellipticdifferentialequation |