Uniqueness of positive solutions to some coupled cooperative variational elliptic systems

An, Yulian; Chern, Jann-Long; Shi, Junping

doi:10.1090/tran/7207

Uniqueness of positive solutions to some coupled cooperative variational elliptic systems
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by Yulian An, Jann-Long Chern and Junping Shi PDF

Trans. Amer. Math. Soc. 370 (2018), 5209-5243 Request permission

Abstract:

The uniqueness of positive solutions to some semilinear elliptic systems with variational structure arising from mathematical physics is proved. The key ingredient of the proof is the oscillatory behavior of solutions to linearized equations for cooperative semilinear elliptic systems of two equations on one-dimensional domains, and it is shown that the stability of the positive solutions for such a semilinear system is closely related to the oscillatory behavior.

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