Existence of solutions to nonlocal and singular elliptic problems via Galerkin method
We study the existence of solutions to the nonlocal elliptic equation $$ -M(|u|^2)Delta u = f(x,u) $$ with zero Dirichlet boundary conditions on a bounded and smooth domain of $mathbb{R}^n$. We consider the $M$-linear case with $fin H^{-1}(Omega )$, and the sub-linear case $f(u)=u^{alpha}$, $0<al...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2004-02-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2004/19/abstr.html |
| _version_ | 1819176127463161856 |
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| author | Francisco Julio S. A. Correa Silvano D. B. Menezes |
| author_facet | Francisco Julio S. A. Correa Silvano D. B. Menezes |
| author_sort | Francisco Julio S. A. Correa |
| collection | DOAJ |
| description | We study the existence of solutions to the nonlocal elliptic equation $$ -M(|u|^2)Delta u = f(x,u) $$ with zero Dirichlet boundary conditions on a bounded and smooth domain of $mathbb{R}^n$. We consider the $M$-linear case with $fin H^{-1}(Omega )$, and the sub-linear case $f(u)=u^{alpha}$, $0<alpha <1$. Our main tool is the Galerkin method for both cases when $M$ continuous and when $M$ is discontinuous. |
| first_indexed | 2024-12-22T21:05:49Z |
| format | Article |
| id | doaj.art-c42d36ecd18740f6b61818d0853a9cb2 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-22T21:05:49Z |
| publishDate | 2004-02-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-c42d36ecd18740f6b61818d0853a9cb22022-12-21T18:12:40ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912004-02-01200419110Existence of solutions to nonlocal and singular elliptic problems via Galerkin methodFrancisco Julio S. A. CorreaSilvano D. B. MenezesWe study the existence of solutions to the nonlocal elliptic equation $$ -M(|u|^2)Delta u = f(x,u) $$ with zero Dirichlet boundary conditions on a bounded and smooth domain of $mathbb{R}^n$. We consider the $M$-linear case with $fin H^{-1}(Omega )$, and the sub-linear case $f(u)=u^{alpha}$, $0<alpha <1$. Our main tool is the Galerkin method for both cases when $M$ continuous and when $M$ is discontinuous.http://ejde.math.txstate.edu/Volumes/2004/19/abstr.htmlNonlocal elliptic problemsGalerkin Method. |
| spellingShingle | Francisco Julio S. A. Correa Silvano D. B. Menezes Existence of solutions to nonlocal and singular elliptic problems via Galerkin method Electronic Journal of Differential Equations Nonlocal elliptic problems Galerkin Method. |
| title | Existence of solutions to nonlocal and singular elliptic problems via Galerkin method |
| title_full | Existence of solutions to nonlocal and singular elliptic problems via Galerkin method |
| title_fullStr | Existence of solutions to nonlocal and singular elliptic problems via Galerkin method |
| title_full_unstemmed | Existence of solutions to nonlocal and singular elliptic problems via Galerkin method |
| title_short | Existence of solutions to nonlocal and singular elliptic problems via Galerkin method |
| title_sort | existence of solutions to nonlocal and singular elliptic problems via galerkin method |
| topic | Nonlocal elliptic problems Galerkin Method. |
| url | http://ejde.math.txstate.edu/Volumes/2004/19/abstr.html |
| work_keys_str_mv | AT franciscojuliosacorrea existenceofsolutionstononlocalandsingularellipticproblemsviagalerkinmethod AT silvanodbmenezes existenceofsolutionstononlocalandsingularellipticproblemsviagalerkinmethod |