Existence, characterization and number of ground states for coupled equations
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This article concerns the existence, characterization and number of ground states for the system consisting of m coupled semilinear equations
-∆ui + λui = m∑j=1 kij qij / p+1 |uj|pij|ui|qij-2ui, x ∈ Ω,
ui ∈ H10(Ω), i = 1, 2, ..., m.
We extend the characterization results obtained by Correia [5, 6] to the above problem. Also we give a new characterization of the ground states, which provides a more convenient way for finding or checking ground states. This study may be the first result not only positive ground states but also for semi-trivial ground states, and it shows that the positive ground state is unique for some special cases.
CitationHe, Q., & Peng, S. (2019). Existence, characterization and number of ground states for coupled equations. Electronic Journal of Differential Equations, 2019(127), pp. 1-18.
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