Existence of Solutions for a Modified Nonlinear Schrödinger System
We are concerned with the following modified nonlinear Schrödinger system: -Δu+u-(1/2)uΔ(u2)=(2α/(α+β))|u|α-2|v|βu, x∈Ω, -Δv+v-(1/2)vΔ(v2)=(2β/(α+β))|u|α|v|β-2v, x∈Ω, u=0, v=0, x∈∂Ω, where α>2, β>2, α+β<2·2*, 2*=2N/(N-2) is the critical...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/431672 |
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| author | Yujuan Jiao Yanli Wang |
| author_facet | Yujuan Jiao Yanli Wang |
| author_sort | Yujuan Jiao |
| collection | DOAJ |
| description | We are concerned with the following modified nonlinear Schrödinger system:
-Δu+u-(1/2)uΔ(u2)=(2α/(α+β))|u|α-2|v|βu, x∈Ω, -Δv+v-(1/2)vΔ(v2)=(2β/(α+β))|u|α|v|β-2v, x∈Ω, u=0, v=0, x∈∂Ω, where α>2, β>2, α+β<2·2*, 2*=2N/(N-2) is the critical Sobolev exponent, and Ω⊂ℝN (N≥3) is a bounded smooth domain. By using the perturbation method, we establish the existence of both positive and negative solutions for this system. |
| format | Article |
| id | doaj-art-34097ec5c5f643c9b6124f7216cf4f93 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-34097ec5c5f643c9b6124f7216cf4f932025-08-20T03:55:15ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/431672431672Existence of Solutions for a Modified Nonlinear Schrödinger SystemYujuan Jiao0Yanli Wang1College of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou 730124, ChinaSchool of Mathematical Sciences, Beijing Normal University, Beijing 100875, ChinaWe are concerned with the following modified nonlinear Schrödinger system: -Δu+u-(1/2)uΔ(u2)=(2α/(α+β))|u|α-2|v|βu, x∈Ω, -Δv+v-(1/2)vΔ(v2)=(2β/(α+β))|u|α|v|β-2v, x∈Ω, u=0, v=0, x∈∂Ω, where α>2, β>2, α+β<2·2*, 2*=2N/(N-2) is the critical Sobolev exponent, and Ω⊂ℝN (N≥3) is a bounded smooth domain. By using the perturbation method, we establish the existence of both positive and negative solutions for this system.http://dx.doi.org/10.1155/2013/431672 |
| spellingShingle | Yujuan Jiao Yanli Wang Existence of Solutions for a Modified Nonlinear Schrödinger System Journal of Applied Mathematics |
| title | Existence of Solutions for a Modified Nonlinear Schrödinger System |
| title_full | Existence of Solutions for a Modified Nonlinear Schrödinger System |
| title_fullStr | Existence of Solutions for a Modified Nonlinear Schrödinger System |
| title_full_unstemmed | Existence of Solutions for a Modified Nonlinear Schrödinger System |
| title_short | Existence of Solutions for a Modified Nonlinear Schrödinger System |
| title_sort | existence of solutions for a modified nonlinear schrodinger system |
| url | http://dx.doi.org/10.1155/2013/431672 |
| work_keys_str_mv | AT yujuanjiao existenceofsolutionsforamodifiednonlinearschrodingersystem AT yanliwang existenceofsolutionsforamodifiednonlinearschrodingersystem |