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- W3119493611 abstract "We look for least energy solutions to the cooperative systems of coupled Schrodinger equations begin{equation*} begin{cases} -Delta u_i + lambda_i u_i = partial_iG(u)quad mathrm{in} mathbb{R}^N, N geq 3, u_i in H^1(mathbb{R}^N), int_{mathbb{R}^N} |u_i|^2 , dx leq rho_i^2 end{cases} iin{1,dots,K} end{equation*} with $Ggeq 0$, where $rho_i>0$ is prescribed and $(lambda_i, u_i) in mathbb{R} times H^1 (mathbb{R}^N)$ is to be determined, $iin{1,dots,K}$. Our approach is based on the minimization of the energy functional over a linear combination of the Nehari and Pohožaev constraints intersected with the product of the closed balls in $L^2(mathbb{R}^N)$ of radii $rho_i$, which allows to provide general growth assumptions about $G$ and to know in advance the sign of the corresponding Lagrange multipliers. We assume that $G$ has at least $L^2$-critical growth at $0$ and admits Sobolev critical growth. The more assumptions we make about $G$, $N$, and $K$, the more can be said about the minimizers of the corresponding energy functional. In particular, if $K=2$, $Nin{3,4}$, and $G$ satisfies further assumptions, then $u=(u_1,u_2)$ is normalized, i.e., $int_{mathbb{R}^N} |u_i|^2 , dx=rho_i^2$ for $iin{1,2}$." @default.
- W3119493611 created "2021-01-18" @default.
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- W3119493611 date "2021-01-07" @default.
- W3119493611 modified "2023-09-27" @default.
- W3119493611 title "Least energy solutions to a cooperative system of Schrodinger equations with prescribed $L^2$-bounds: at least $L^2$-critical growth" @default.
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