Nonexistence of nonnegative entire solutions of semilinear elliptic\n systems

2020/03/03 by Alexander Gladkov, Gladkov, Alexander, Sergey Sergeenko +1
Mathematics · #35J47 #35J91 #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #FOS: Mathematics #Meromorphic and Entire Functions #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2003.01372

openalex publication_date 2020/03/03 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We consider the second order semilinear elliptic system\n \Δ u= p\( x\) v^\α, \Δ v= q\(x\) u^\β,\nwhere\n x \∈ \R^N, N \≥ 3, \α and \β are positive\nconstants,\n p and q are nonnegative continuous functions. We prove that nontrivial\nnonnegative entire solutions\n fail to exist if the functions p and q are of slow decay.\n

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