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Cauchy problem of semilinear inhomogeneous elliptic equations of Matukuma-type with multiple growth terms

  • * Corresponding author: Yi Li

    * Corresponding author: Yi Li 

Y. Jia and J. Wu are supported in part by the Natural Science Foundations of China (11771262, 11671243, 61672021), by the Natural Science Basic Research Plan in Shaanxi Province of China (2018JM1020)

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  • We consider the structure and the stability of positive radial solutions of a semilinear inhomogeneous elliptic equation with multiple growth terms

    $ \Delta u+\sum\limits_{i = 1}^{k}K_i(|x|)u^{p_i}+\mu f(|x|) = 0, \quad x\in\mathbb{R}^n, $

    which is a generalization of Matukuma's equation describing the dynamics of a globular cluster of stars. Equations similar to this kind have come up both in geometry and in physics, and have been a subject of extensive studies. Our result shows that any positive radial solution is stable or weakly asymptotically stable with respect to certain norm.

    Mathematics Subject Classification: Primary: 35J10, 35J20; Secondary: 35J65.

    Citation:

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