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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |