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Liouville‐type results for a class of quasilinear elliptic systems and applications
Author(s) -
Dancer E. N.,
Yang Hui,
Zou Wenming
Publication year - 2019
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms.12170
Subject(s) - type (biology) , singularity , operator (biology) , laplace operator , a priori and a posteriori , class (philosophy) , mathematics , schrödinger's cat , pure mathematics , mathematical physics , mathematical analysis , physics , computer science , chemistry , artificial intelligence , ecology , biochemistry , philosophy , epistemology , repressor , gene , transcription factor , biology
In this paper, we study the following quasilinear elliptic systems− Δ m u = f 1 ( u , v )i nR N ,− Δ m v = f 2 ( u , v )i nR N .Here Δ m is the well‐known m ‐Laplacian operator, m > 1 . Under appropriate conditions on the functions f 1 and f 2 , we prove some Liouville‐type nonexistence theorems. The Liouville‐type results can be applied to non‐cooperative quasilinear Schrödinger‐type systems, and we obtain a priori estimates, singularity and decay estimates for the non‐negative solutions of the non‐cooperative quasilinear Schrödinger‐type systems.