A condition on the potential for the existence of doubly periodic solutions of a semi-linear fourth-order partial differential equation
We study the existence of solutions to the fourth order semi-linear equation $Delta ^2u=g(u)+h(x)$. We show that there is a positive constant $C_*$, such that if $g(xi )xi geq 0$ for $|xi |geq xi _0$ and $limsup _{|xi |o infty } 2G(xi )/xi^2<C_*$, then for all $hin L^2(Q)$ with $int _Q h dx=0$, t...
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| Format: | Article |
| Language: | English |
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Texas State University
2000-10-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/conf-proc/05/c4/abstr.html |
| _version_ | 1811277378425454592 |
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| author | Chen Chang |
| author_facet | Chen Chang |
| author_sort | Chen Chang |
| collection | DOAJ |
| description | We study the existence of solutions to the fourth order semi-linear equation $Delta ^2u=g(u)+h(x)$. We show that there is a positive constant $C_*$, such that if $g(xi )xi geq 0$ for $|xi |geq xi _0$ and $limsup _{|xi |o infty } 2G(xi )/xi^2<C_*$, then for all $hin L^2(Q)$ with $int _Q h dx=0$, the above equation has a weak solution in $H^2_{2pi}$. |
| first_indexed | 2024-04-13T00:14:34Z |
| format | Article |
| id | doaj.art-4568ed9584ae4ef294c23dcd9b94c14d |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-13T00:14:34Z |
| publishDate | 2000-10-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-4568ed9584ae4ef294c23dcd9b94c14d2022-12-22T03:10:58ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912000-10-01Conference05325333A condition on the potential for the existence of doubly periodic solutions of a semi-linear fourth-order partial differential equationChen ChangWe study the existence of solutions to the fourth order semi-linear equation $Delta ^2u=g(u)+h(x)$. We show that there is a positive constant $C_*$, such that if $g(xi )xi geq 0$ for $|xi |geq xi _0$ and $limsup _{|xi |o infty } 2G(xi )/xi^2<C_*$, then for all $hin L^2(Q)$ with $int _Q h dx=0$, the above equation has a weak solution in $H^2_{2pi}$.http://ejde.math.txstate.edu/conf-proc/05/c4/abstr.htmlperiodic solutionselliptic fourth-order PDE. |
| spellingShingle | Chen Chang A condition on the potential for the existence of doubly periodic solutions of a semi-linear fourth-order partial differential equation Electronic Journal of Differential Equations periodic solutions elliptic fourth-order PDE. |
| title | A condition on the potential for the existence of doubly periodic solutions of a semi-linear fourth-order partial differential equation |
| title_full | A condition on the potential for the existence of doubly periodic solutions of a semi-linear fourth-order partial differential equation |
| title_fullStr | A condition on the potential for the existence of doubly periodic solutions of a semi-linear fourth-order partial differential equation |
| title_full_unstemmed | A condition on the potential for the existence of doubly periodic solutions of a semi-linear fourth-order partial differential equation |
| title_short | A condition on the potential for the existence of doubly periodic solutions of a semi-linear fourth-order partial differential equation |
| title_sort | condition on the potential for the existence of doubly periodic solutions of a semi linear fourth order partial differential equation |
| topic | periodic solutions elliptic fourth-order PDE. |
| url | http://ejde.math.txstate.edu/conf-proc/05/c4/abstr.html |
| work_keys_str_mv | AT chenchang aconditiononthepotentialfortheexistenceofdoublyperiodicsolutionsofasemilinearfourthorderpartialdifferentialequation AT chenchang conditiononthepotentialfortheexistenceofdoublyperiodicsolutionsofasemilinearfourthorderpartialdifferentialequation |