关于具有次线性竞争相互作用的椭圆型系统中死核的出现
On the emergence of dead cores in elliptic systems with sublinear competitive interactions
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中文总结 AI 辅助
研究具有次线性耦合项的半线性椭圆型系统，利用次线性方程下解有死核及一致赫尔德界的结论，证明竞争型相互作用下解有死核，并应用于多种解，如基态和最小能量变号解。
中文摘要 AI 辅助
本文研究具有次线性耦合项的半线性椭圆型系统，表明在竞争型相互作用下，解通常具有死核，即在区域的某些开子集上消失。我们将结果应用于文献中处理的一大类解，如狄利克雷边界条件下或全空间中的基态和最小能量变号解。证明基于一个一般结果，即某个次线性方程的下解有死核，以及一致赫尔德界。
英文摘要
In this paper, we study semilinear elliptic systems with sublinear coupling terms, showing that, under competition-type interactions, solutions typically have dead cores, i.e., they vanish on certain open subsets of the domain. We apply our results to a large class of solutions treated in the literature, for instance to ground states and least energy sign-changing solutions, under Dirichlet boundary conditions or in the whole space. The proofs are based on a general result stating that subsolutions to a certain sublinear equation have dead cores, and on uniform Hölder bounds.
