| Popis: |
We study the existence of standing wave solutions of the complex Ginzburg–Landau equation (GL) φ t − e i θ ( ρ I − Δ ) φ − e i γ | φ | α φ = 0 in R N , where α > 0 , ( N − 2 ) α 4 , ρ > 0 and θ , γ ∈ R . We show that for any θ ∈ ( − π / 2 , π / 2 ) there exists e > 0 such that (GL) has a non-trivial standing wave solution if | γ − θ | e . Analogous result is obtained in a ball Ω ∈ R N for ρ > − λ 1 , where λ 1 is the first eigenvalue of the Laplace operator with Dirichlet boundary conditions. |
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