Existence and multiplicity of solutions for a differential inclusion problem involving the p(x)-Laplacian
In this article we consider the differential inclusion $$displaylines{ -hbox{div}(| abla u|^{p(x)-2} abla u)in partial F(x,u) quadhbox{in }Omega,cr u=0 quad hbox{on }partial Omega }$$ which involves the $p(x)$-Laplacian. By applying the nonsmooth Mountain Pass Theorem, we obtain at least one...
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| Format: | Article |
| Language: | English |
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Texas State University
2010-03-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2010/44/abstr.html |
| _version_ | 1818064714415996928 |
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| author | Guowei Dai |
| author_facet | Guowei Dai |
| author_sort | Guowei Dai |
| collection | DOAJ |
| description | In this article we consider the differential inclusion $$displaylines{ -hbox{div}(| abla u|^{p(x)-2} abla u)in partial F(x,u) quadhbox{in }Omega,cr u=0 quad hbox{on }partial Omega }$$ which involves the $p(x)$-Laplacian. By applying the nonsmooth Mountain Pass Theorem, we obtain at least one nontrivial solution; and by applying the symmetric Mountain Pass Theorem, we obtain k-pairs of nontrivial solutions in $W_{0}^{1,p(x)}(Omega)$. |
| first_indexed | 2024-12-10T14:40:23Z |
| format | Article |
| id | doaj.art-86c2caf8ac1b433f828077c466980cb6 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-10T14:40:23Z |
| publishDate | 2010-03-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-86c2caf8ac1b433f828077c466980cb62022-12-22T01:44:42ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912010-03-01201044,19Existence and multiplicity of solutions for a differential inclusion problem involving the p(x)-LaplacianGuowei DaiIn this article we consider the differential inclusion $$displaylines{ -hbox{div}(| abla u|^{p(x)-2} abla u)in partial F(x,u) quadhbox{in }Omega,cr u=0 quad hbox{on }partial Omega }$$ which involves the $p(x)$-Laplacian. By applying the nonsmooth Mountain Pass Theorem, we obtain at least one nontrivial solution; and by applying the symmetric Mountain Pass Theorem, we obtain k-pairs of nontrivial solutions in $W_{0}^{1,p(x)}(Omega)$.http://ejde.math.txstate.edu/Volumes/2010/44/abstr.htmlp(x)-Laplaciannonsmooth mountain pass theoremdifferential inclusion |
| spellingShingle | Guowei Dai Existence and multiplicity of solutions for a differential inclusion problem involving the p(x)-Laplacian Electronic Journal of Differential Equations p(x)-Laplacian nonsmooth mountain pass theorem differential inclusion |
| title | Existence and multiplicity of solutions for a differential inclusion problem involving the p(x)-Laplacian |
| title_full | Existence and multiplicity of solutions for a differential inclusion problem involving the p(x)-Laplacian |
| title_fullStr | Existence and multiplicity of solutions for a differential inclusion problem involving the p(x)-Laplacian |
| title_full_unstemmed | Existence and multiplicity of solutions for a differential inclusion problem involving the p(x)-Laplacian |
| title_short | Existence and multiplicity of solutions for a differential inclusion problem involving the p(x)-Laplacian |
| title_sort | existence and multiplicity of solutions for a differential inclusion problem involving the p x laplacian |
| topic | p(x)-Laplacian nonsmooth mountain pass theorem differential inclusion |
| url | http://ejde.math.txstate.edu/Volumes/2010/44/abstr.html |
| work_keys_str_mv | AT guoweidai existenceandmultiplicityofsolutionsforadifferentialinclusionprobleminvolvingthepxlaplacian |