Nodal solutions for nonlinear Schrodinger systems

In this article we consider the nonlinear Schrodinger system - Δ uⱼ + λⱼ uⱼ = ∑ᵢ₌₁ᵏ βᵢⱼ uᵢ² uⱼ, in Ω, uⱼ ( x ) = 0, on ∂ Ω , \; j=1,l,k , where \(Ω⊂ R^N \) (\(N=2,3\)) is a bounded smooth domain, \(λ_j> 0\), \(j=1,…,k\), \(βᵢⱼ\) are constants satisfying \(βⱼⱼ>0\), \(βᵢⱼ=βⱼᵢ≤ 0 \) for \(1≤ i< j≤ k\). The existence of sign-changing solutions is proved by the truncation method and the invariant sets of descending flow method. For more information see https://ejde.math.txstate.edu/Volumes/2024/31/abstr.html