Multiplicity of Solutions for a Class of Fourth-Order Elliptic Problems with Asymptotically Linear Term
We study the following fourth-order elliptic equations: Δ2𝑢+𝑎Δ𝑢=𝑓(𝑥,𝑢),𝑥∈Ω,𝑢=Δ𝑢=0,𝑥∈𝜕Ω, where Ω⊂ℝ𝑁 is a bounded domain with smooth boundary 𝜕Ω and 𝑓(𝑥,𝑢) is asymptotically linear with respect to 𝑢 at infinity. Using an equivalent version of Cerami's condition and the symmetric mountain pass lem...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/749059 |
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| author | Qiong Liu Dengfeng Lü |
| author_facet | Qiong Liu Dengfeng Lü |
| author_sort | Qiong Liu |
| collection | DOAJ |
| description | We study the following fourth-order elliptic equations: Δ2𝑢+𝑎Δ𝑢=𝑓(𝑥,𝑢),𝑥∈Ω,𝑢=Δ𝑢=0,𝑥∈𝜕Ω, where Ω⊂ℝ𝑁 is a bounded domain with smooth boundary 𝜕Ω and 𝑓(𝑥,𝑢) is asymptotically linear with respect to 𝑢 at infinity. Using an equivalent version of Cerami's condition and the symmetric mountain pass lemma, we obtain the existence of multiple solutions for the equations. |
| format | Article |
| id | doaj-art-066ebd938d9f4e958e734dcd03e24e85 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-066ebd938d9f4e958e734dcd03e24e852025-02-03T06:07:12ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/749059749059Multiplicity of Solutions for a Class of Fourth-Order Elliptic Problems with Asymptotically Linear TermQiong Liu0Dengfeng Lü1School of Mathematics and Statistics, Hubei Engineering University, Hubei, Xiaogan 432000, ChinaSchool of Mathematics and Statistics, Hubei Engineering University, Hubei, Xiaogan 432000, ChinaWe study the following fourth-order elliptic equations: Δ2𝑢+𝑎Δ𝑢=𝑓(𝑥,𝑢),𝑥∈Ω,𝑢=Δ𝑢=0,𝑥∈𝜕Ω, where Ω⊂ℝ𝑁 is a bounded domain with smooth boundary 𝜕Ω and 𝑓(𝑥,𝑢) is asymptotically linear with respect to 𝑢 at infinity. Using an equivalent version of Cerami's condition and the symmetric mountain pass lemma, we obtain the existence of multiple solutions for the equations.http://dx.doi.org/10.1155/2012/749059 |
| spellingShingle | Qiong Liu Dengfeng Lü Multiplicity of Solutions for a Class of Fourth-Order Elliptic Problems with Asymptotically Linear Term Journal of Applied Mathematics |
| title | Multiplicity of Solutions for a Class of Fourth-Order Elliptic Problems with Asymptotically Linear Term |
| title_full | Multiplicity of Solutions for a Class of Fourth-Order Elliptic Problems with Asymptotically Linear Term |
| title_fullStr | Multiplicity of Solutions for a Class of Fourth-Order Elliptic Problems with Asymptotically Linear Term |
| title_full_unstemmed | Multiplicity of Solutions for a Class of Fourth-Order Elliptic Problems with Asymptotically Linear Term |
| title_short | Multiplicity of Solutions for a Class of Fourth-Order Elliptic Problems with Asymptotically Linear Term |
| title_sort | multiplicity of solutions for a class of fourth order elliptic problems with asymptotically linear term |
| url | http://dx.doi.org/10.1155/2012/749059 |
| work_keys_str_mv | AT qiongliu multiplicityofsolutionsforaclassoffourthorderellipticproblemswithasymptoticallylinearterm AT dengfenglu multiplicityofsolutionsforaclassoffourthorderellipticproblemswithasymptoticallylinearterm |