We prove the existence of a positive radial solution for the Henon equation with arbitrary growth. The solution is found by means of a shooting method and turns out to be an increasing function of the radial variable. Some numerical experiments suggest the existence of many positive oscillating solutions.
Barutello, V., Secchi, S., Serra, E. (2008). A note on the radial solutions for the supercritical Hénon equation. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 341(1), 720-728 [10.1016/j.jmaa.2007.10.052].
A note on the radial solutions for the supercritical Hénon equation
SECCHI, SIMONE;
2008
Abstract
We prove the existence of a positive radial solution for the Henon equation with arbitrary growth. The solution is found by means of a shooting method and turns out to be an increasing function of the radial variable. Some numerical experiments suggest the existence of many positive oscillating solutions.
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