Existence of Solutions for a Modified Nonlinear Schrödinger System
Keyword(s):
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, whereα>2, β>2, α+β<2·2*, 2*=2N/(N-2)is the critical Sobolev exponent, andΩ⊂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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