We prove the existence of infinitely many solutions λ1, λ2∈ R, u, v∈ H1(R3), for the nonlinear Schrödinger system -Δu-λ1u=μu3+βuv2inR3-Δv-λ2v=μv3+βu2vinR3u,v>0inR3∫R3u2=a2and∫R3v2=a2,where a, μ> 0 and β≤ - μ are prescribed. Our solutions satisfy u≠ v so they do not come from a scalar equation. The proof is based on a new minimax argument, suited to deal with normalization conditions.
Multiple normalized solutions for a competing system of Schrödinger equations
Soave, Nicola
2019-01-01
Abstract
We prove the existence of infinitely many solutions λ1, λ2∈ R, u, v∈ H1(R3), for the nonlinear Schrödinger system -Δu-λ1u=μu3+βuv2inR3-Δv-λ2v=μv3+βu2vinR3u,v>0inR3∫R3u2=a2and∫R3v2=a2,where a, μ> 0 and β≤ - μ are prescribed. Our solutions satisfy u≠ v so they do not come from a scalar equation. The proof is based on a new minimax argument, suited to deal with normalization conditions.File in questo prodotto:
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