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• W2963165669 startingPage "3277" @default.
• W2963165669 abstract "In this paper, we establish the sharp criteria for thenonexistence of positive solutions to the Hardy-Littlewood-Sobolev(HLS) system of nonlinear equations and the correspondingnonlinear differential systems of Lane-Emden type. Thesenonexistence results, known as Liouville theorems, arefundamental in PDE theory and applications. A special iterationscheme, a new shooting method and some Pohozaev identities inintegral form as well as in differential form are created.Combining these new techniques with some observations and somecritical asymptotic analysis, we establish the sharp criteria ofLiouville type for our systems of nonlinear equations. Similarresults are also derived for the system of Wolff type of integralequations and the system of $gamma$-Laplace equations. Adichotomy description in terms of existence and nonexistence forsolutions with finite energy is also obtained." @default.
• W2963165669 created "2019-07-30" @default.
• W2963165669 creator A5018643424 @default.
• W2963165669 creator A5080498499 @default.
• W2963165669 date "2015-12-01" @default.
• W2963165669 modified "2023-10-17" @default.
• W2963165669 title "Sharp criteria of Liouville type for some nonlinear systems" @default.
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• W2963165669 doi "https://doi.org/10.3934/dcds.2016.36.3277" @default.
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