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- W3157057362 abstract "We study the existence of solutions to the cubic Schrodinger system $$ -Delta = sum_{j =1}^m beta_{ij} u_j^2u_i + lambda_i u_i hbox{in} Omega, u_i=0 hbox{on} partialOmega, i =1,dots,m, $$ when $Omega$ is a bounded domain in $mathbb R^4, $ $lambda_i$ are positive small numbers, $beta_{ij}$ are real numbers so that $beta_{ii}>0$ and $beta_{ij}=beta_{ji}$, $ineq j$. We assemble the components $u_i$ in groups so that all the interaction forces $beta_{ij}$ among components of the same group are attractive, i.e. $beta_{ij}>0$, while forces among components of different groups are repulsive or weakly attractive, i.e. $beta_{ij}<overlinebeta$ for some $overlinebeta$ small. We find solutions such that each component within a given group blows-up around the same point and the different groups blow-up around different points, as all the parameters $lambda_i$'s approach zero." @default.
- W3157057362 created "2021-05-10" @default.
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- W3157057362 date "2021-04-30" @default.
- W3157057362 modified "2023-09-27" @default.
- W3157057362 title "Solutions to a cubic Schrodinger system with mixed attractive and repulsive forces in a critical regime." @default.
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