Multiple Positive Solutions of Nonhomogeneous Elliptic Equations in Unbounded Domains
We will show that under suitable conditions on f and h, there exists a positive number λ∗ such that the nonhomogeneous elliptic equation −Δu+u=λ(f(x,u)+h(x)) in Ω, u∈H01(Ω), N≥2, has at least two positive solutions if λ∈(0,λ∗), a unique positive solution if λ=λ∗, and no positive solution if λ>λ∗...
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2007/43018 |
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| _version_ | 1832559476027162624 |
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| author | Tsing-San Hsu |
| author_facet | Tsing-San Hsu |
| author_sort | Tsing-San Hsu |
| collection | DOAJ |
| description | We will show that under suitable conditions on f and h, there exists a positive number λ∗ such that the nonhomogeneous elliptic equation
−Δu+u=λ(f(x,u)+h(x)) in Ω, u∈H01(Ω), N≥2, has at least two positive solutions if λ∈(0,λ∗), a unique positive solution if λ=λ∗, and no positive solution if λ>λ∗, where Ω is the entire space or an exterior domain or an unbounded cylinder domain
or the complement in a strip domain of a bounded domain.
We also obtain some properties of the set of solutions. |
| format | Article |
| id | doaj-art-2bf0f33bd4c543b2b2e4e55acc881739 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-2bf0f33bd4c543b2b2e4e55acc8817392025-02-03T01:29:57ZengWileyAbstract and Applied Analysis1085-33751687-04092007-01-01200710.1155/2007/4301843018Multiple Positive Solutions of Nonhomogeneous Elliptic Equations in Unbounded DomainsTsing-San Hsu0Center for General Education, Chang Gung University, Kwei-Shan, Tao-Yuan 333, TaiwanWe will show that under suitable conditions on f and h, there exists a positive number λ∗ such that the nonhomogeneous elliptic equation −Δu+u=λ(f(x,u)+h(x)) in Ω, u∈H01(Ω), N≥2, has at least two positive solutions if λ∈(0,λ∗), a unique positive solution if λ=λ∗, and no positive solution if λ>λ∗, where Ω is the entire space or an exterior domain or an unbounded cylinder domain or the complement in a strip domain of a bounded domain. We also obtain some properties of the set of solutions.http://dx.doi.org/10.1155/2007/43018 |
| spellingShingle | Tsing-San Hsu Multiple Positive Solutions of Nonhomogeneous Elliptic Equations in Unbounded Domains Abstract and Applied Analysis |
| title | Multiple Positive Solutions of Nonhomogeneous Elliptic Equations in Unbounded Domains |
| title_full | Multiple Positive Solutions of Nonhomogeneous Elliptic Equations in Unbounded Domains |
| title_fullStr | Multiple Positive Solutions of Nonhomogeneous Elliptic Equations in Unbounded Domains |
| title_full_unstemmed | Multiple Positive Solutions of Nonhomogeneous Elliptic Equations in Unbounded Domains |
| title_short | Multiple Positive Solutions of Nonhomogeneous Elliptic Equations in Unbounded Domains |
| title_sort | multiple positive solutions of nonhomogeneous elliptic equations in unbounded domains |
| url | http://dx.doi.org/10.1155/2007/43018 |
| work_keys_str_mv | AT tsingsanhsu multiplepositivesolutionsofnonhomogeneousellipticequationsinunboundeddomains |