Multiple solutions for singularly perturbed semilinear elliptic equations in bounded domains
We are concerned with the multiplicity of solutions of the following singularly perturbed semilinear elliptic equations in bounded domains Ω:−ε2Δu+a(⋅)u=u|u|p−2 in Ω, u>0 in Ω, u=0 on ∂Ω. The main purpose of this paper is to discuss the relationship between the multiplicity of solutions and the...
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/AAA.2005.185 |
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| _version_ | 1832558080591659008 |
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| author | Michinori Ishiwata |
| author_facet | Michinori Ishiwata |
| author_sort | Michinori Ishiwata |
| collection | DOAJ |
| description | We are concerned with the multiplicity of solutions of the
following singularly perturbed semilinear elliptic equations
in bounded domains Ω:−ε2Δu+a(⋅)u=u|u|p−2 in Ω, u>0 in Ω, u=0 on ∂Ω. The main purpose of this
paper is to discuss the relationship between the multiplicity of
solutions and the profile of a(⋅) from the variational point
of view. It is shown that if a has a “peak” in Ω, then (P) has at least three solutions for sufficiently small ε. |
| format | Article |
| id | doaj-art-0d5dd82b139344d6881846fda60ddaa6 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-0d5dd82b139344d6881846fda60ddaa62025-02-03T01:33:13ZengWileyAbstract and Applied Analysis1085-33751687-04092005-01-012005218520510.1155/AAA.2005.185Multiple solutions for singularly perturbed semilinear elliptic equations in bounded domainsMichinori Ishiwata0Department of Mathematical Sciences, School of Science and Engineering, Waseda University, 3-4-1 Okubo Shinjuku-ku, Tokyo 169-8555, JapanWe are concerned with the multiplicity of solutions of the following singularly perturbed semilinear elliptic equations in bounded domains Ω:−ε2Δu+a(⋅)u=u|u|p−2 in Ω, u>0 in Ω, u=0 on ∂Ω. The main purpose of this paper is to discuss the relationship between the multiplicity of solutions and the profile of a(⋅) from the variational point of view. It is shown that if a has a “peak” in Ω, then (P) has at least three solutions for sufficiently small ε.http://dx.doi.org/10.1155/AAA.2005.185 |
| spellingShingle | Michinori Ishiwata Multiple solutions for singularly perturbed semilinear elliptic equations in bounded domains Abstract and Applied Analysis |
| title | Multiple solutions for singularly perturbed
semilinear elliptic equations in bounded domains |
| title_full | Multiple solutions for singularly perturbed
semilinear elliptic equations in bounded domains |
| title_fullStr | Multiple solutions for singularly perturbed
semilinear elliptic equations in bounded domains |
| title_full_unstemmed | Multiple solutions for singularly perturbed
semilinear elliptic equations in bounded domains |
| title_short | Multiple solutions for singularly perturbed
semilinear elliptic equations in bounded domains |
| title_sort | multiple solutions for singularly perturbed semilinear elliptic equations in bounded domains |
| url | http://dx.doi.org/10.1155/AAA.2005.185 |
| work_keys_str_mv | AT michinoriishiwata multiplesolutionsforsingularlyperturbedsemilinearellipticequationsinboundeddomains |