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Classification of solutions to a system of $ n^{\rm th} $ order equations on $ \mathbb R^n $

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  • This work concerns the distributional solutions of a conformally invariant system of $ n^{\rm th} $-order elliptic equations on $ \mathbb R^n $ having exponential type nonlinearity. The system in question is a natural generalization of the constant $ Q $-curvature equation on $ \mathbb R^n $. Under an $ L^1 $-finiteness assumption and some assumptions on the coupling coefficients, an asymptotic estimate for solutions as $ \left|x\right|\to \infty $ is obtained. Under a growth constraint and further $ L^1 $-norm assumptions the method of moving spheres is used to show that, up to an additive polynomial of low degree, each of the unknown functions is a standard bubble with common center and scale parameters.

    Mathematics Subject Classification: 35C05, 35G50, 35J48.


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