Twin Positive Solutions for Schrödinger-Kirchhoff-Type Problem with Singularity and Critical Exponents
We study in this paper the following singular Schrödinger-Kirchhoff-type problem with critical exponent -a+b∫Ω∇u2dxΔu+u=Q(x)u5+μxα-2u+f(x)(λ/uγ) in Ω,u=0 on ∂Ω, where a,b>0 are constants, Ω⊂R3 is a smooth bounded domain, 0<α<1, λ>0 is a real parameter, γ∈(0,1) is a constant, and 0<μ&l...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/6108538 |
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| _version_ | 1850161660194455552 |
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| author | Wei Han Yangyang Zhao |
| author_facet | Wei Han Yangyang Zhao |
| author_sort | Wei Han |
| collection | DOAJ |
| description | We study in this paper the following singular Schrödinger-Kirchhoff-type problem with critical exponent -a+b∫Ω∇u2dxΔu+u=Q(x)u5+μxα-2u+f(x)(λ/uγ) in Ω,u=0 on ∂Ω, where a,b>0 are constants, Ω⊂R3 is a smooth bounded domain, 0<α<1, λ>0 is a real parameter, γ∈(0,1) is a constant, and 0<μ<aμ1 (μ1 is the first eigenvalue of -Δu=μxα-2u, under Dirichlet boundary condition). Under appropriate assumptions on Q and f, we obtain two positive solutions via the variational and perturbation methods. |
| format | Article |
| id | doaj-art-ff0cf4561e8d44c99bba8dd09f1166c7 |
| institution | OA Journals |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-ff0cf4561e8d44c99bba8dd09f1166c72025-08-20T02:22:45ZengWileyJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/61085386108538Twin Positive Solutions for Schrödinger-Kirchhoff-Type Problem with Singularity and Critical ExponentsWei Han0Yangyang Zhao1Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, ChinaDepartment of Mathematics, North University of China, Taiyuan, Shanxi 030051, ChinaWe study in this paper the following singular Schrödinger-Kirchhoff-type problem with critical exponent -a+b∫Ω∇u2dxΔu+u=Q(x)u5+μxα-2u+f(x)(λ/uγ) in Ω,u=0 on ∂Ω, where a,b>0 are constants, Ω⊂R3 is a smooth bounded domain, 0<α<1, λ>0 is a real parameter, γ∈(0,1) is a constant, and 0<μ<aμ1 (μ1 is the first eigenvalue of -Δu=μxα-2u, under Dirichlet boundary condition). Under appropriate assumptions on Q and f, we obtain two positive solutions via the variational and perturbation methods.http://dx.doi.org/10.1155/2018/6108538 |
| spellingShingle | Wei Han Yangyang Zhao Twin Positive Solutions for Schrödinger-Kirchhoff-Type Problem with Singularity and Critical Exponents Journal of Function Spaces |
| title | Twin Positive Solutions for Schrödinger-Kirchhoff-Type Problem with Singularity and Critical Exponents |
| title_full | Twin Positive Solutions for Schrödinger-Kirchhoff-Type Problem with Singularity and Critical Exponents |
| title_fullStr | Twin Positive Solutions for Schrödinger-Kirchhoff-Type Problem with Singularity and Critical Exponents |
| title_full_unstemmed | Twin Positive Solutions for Schrödinger-Kirchhoff-Type Problem with Singularity and Critical Exponents |
| title_short | Twin Positive Solutions for Schrödinger-Kirchhoff-Type Problem with Singularity and Critical Exponents |
| title_sort | twin positive solutions for schrodinger kirchhoff type problem with singularity and critical exponents |
| url | http://dx.doi.org/10.1155/2018/6108538 |
| work_keys_str_mv | AT weihan twinpositivesolutionsforschrodingerkirchhofftypeproblemwithsingularityandcriticalexponents AT yangyangzhao twinpositivesolutionsforschrodingerkirchhofftypeproblemwithsingularityandcriticalexponents |