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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1110-757X 1687-0042 |