Existence, characterization and number of ground states for coupled equations
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Date
2019-11-26
Authors
He, Qihan
Peng, Shuangjie
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
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.
Description
Keywords
Coupled equations, Ground states
Citation
He, Q., & Peng, S. (2019). Existence, characterization and number of ground states for coupled equations. <i>Electronic Journal of Differential Equations, 2019</i>(127), pp. 1-18.
Rights
Attribution 4.0 International