Nonexistence of nonnegative entire solutions of semilinear elliptic systems

Alexander Gladkov; Sergey Sergeenko

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arXiv · 2003.01372

Nonexistence of nonnegative entire solutions of semilinear elliptic systems

Alexander Gladkov·Sergey Sergeenko

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Abstract

We consider the second order semilinear elliptic system $\Delta u= p\left( x\right) v^\alpha,$ $\Delta v= q\left(x\right) u^\beta,$ where $x \in \mathbf{R}^N,$ $N \geq 3,$ $\alpha$ and $\beta$ are positive constants, $p$ and $q$ are nonnegative continuous functions. We prove that nontrivial nonnegative entire solutions fail to exist if the functions $p$ and $q$ are of slow decay.

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Alexander Gladkov, Sergey Sergeenko. 2020-03-03. Nonexistence of nonnegative entire solutions of semilinear elliptic systems. https://arxiv.org/abs/2003.01372

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