Various Half-Eigenvalues of Scalar p-Laplacian with Indefinite Integrable Weights
Consider the half-eigenvalue problem (ϕp(x′))′+λa(t)ϕp(x+)−λb(t)ϕp(x−)=0 a.e. t∈[0,1], where 1<p<∞, ϕp(x)=|x|p−2x, x±(⋅)=max{±x(⋅), 0} for x∈𝒞0:=C([0,1],ℝ), and a(t) and b(t) are indefinite integrable weights in the Lebesgue space ℒγ:=Lγ([0,1],ℝ),1≤γ≤∞. We characterize the spectr...
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| Language: | English |
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2009-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2009/109757 |
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| author | Wei Li Ping Yan |
| author_facet | Wei Li Ping Yan |
| author_sort | Wei Li |
| collection | DOAJ |
| description | Consider the half-eigenvalue problem (ϕp(x′))′+λa(t)ϕp(x+)−λb(t)ϕp(x−)=0 a.e.
t∈[0,1], where 1<p<∞, ϕp(x)=|x|p−2x, x±(⋅)=max{±x(⋅), 0} for x∈𝒞0:=C([0,1],ℝ), and a(t) and b(t) are indefinite integrable weights in the Lebesgue
space ℒγ:=Lγ([0,1],ℝ),1≤γ≤∞. We characterize the spectra structure under periodic, antiperiodic, Dirichlet, and Neumann boundary conditions, respectively. Furthermore, all these half-eigenvalues are continuous in (a,b)∈(ℒγ,wγ)2, where wγ denotes the weak topology in ℒγ space. The Dirichlet and the Neumann half-eigenvalues are continuously Fréchet differentiable in (a,b)∈(ℒγ,‖⋅‖γ)2, where ‖⋅‖γ is the Lγ norm of ℒγ. |
| format | Article |
| id | doaj-art-7b2c015f8c6b4467bf2bf5a3ffa2e372 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-7b2c015f8c6b4467bf2bf5a3ffa2e3722025-02-03T01:22:39ZengWileyAbstract and Applied Analysis1085-33751687-04092009-01-01200910.1155/2009/109757109757Various Half-Eigenvalues of Scalar p-Laplacian with Indefinite Integrable WeightsWei Li0Ping Yan1Department of Mathematical Sciences, Tsinghua University, Beijing 100084, ChinaDepartment of Mathematical Sciences, Tsinghua University, Beijing 100084, ChinaConsider the half-eigenvalue problem (ϕp(x′))′+λa(t)ϕp(x+)−λb(t)ϕp(x−)=0 a.e. t∈[0,1], where 1<p<∞, ϕp(x)=|x|p−2x, x±(⋅)=max{±x(⋅), 0} for x∈𝒞0:=C([0,1],ℝ), and a(t) and b(t) are indefinite integrable weights in the Lebesgue space ℒγ:=Lγ([0,1],ℝ),1≤γ≤∞. We characterize the spectra structure under periodic, antiperiodic, Dirichlet, and Neumann boundary conditions, respectively. Furthermore, all these half-eigenvalues are continuous in (a,b)∈(ℒγ,wγ)2, where wγ denotes the weak topology in ℒγ space. The Dirichlet and the Neumann half-eigenvalues are continuously Fréchet differentiable in (a,b)∈(ℒγ,‖⋅‖γ)2, where ‖⋅‖γ is the Lγ norm of ℒγ.http://dx.doi.org/10.1155/2009/109757 |
| spellingShingle | Wei Li Ping Yan Various Half-Eigenvalues of Scalar p-Laplacian with Indefinite Integrable Weights Abstract and Applied Analysis |
| title | Various Half-Eigenvalues of Scalar p-Laplacian with Indefinite Integrable Weights |
| title_full | Various Half-Eigenvalues of Scalar p-Laplacian with Indefinite Integrable Weights |
| title_fullStr | Various Half-Eigenvalues of Scalar p-Laplacian with Indefinite Integrable Weights |
| title_full_unstemmed | Various Half-Eigenvalues of Scalar p-Laplacian with Indefinite Integrable Weights |
| title_short | Various Half-Eigenvalues of Scalar p-Laplacian with Indefinite Integrable Weights |
| title_sort | various half eigenvalues of scalar p laplacian with indefinite integrable weights |
| url | http://dx.doi.org/10.1155/2009/109757 |
| work_keys_str_mv | AT weili varioushalfeigenvaluesofscalarplaplacianwithindefiniteintegrableweights AT pingyan varioushalfeigenvaluesofscalarplaplacianwithindefiniteintegrableweights |