TY - JOUR
T1 - Uniqueness of finite total curvatures and the structure of radial solutions for nonlinear elliptic equations
AU - Chern, Jann Long
AU - Chen, Zhi You
AU - Tang, Yong Li
PY - 2011/6
Y1 - 2011/6
N2 - In this article, we are concerned with the semilinear elliptic equation δu + K(|x|)|u|p-1u = 0 in Rn \ {0}, where n > 2, p > 1, and K(|x|) > 0 in Rn. The correspondence between the initial values of regularly positive radial solutions of the above equation and the associated finite total curvatures will be derived. In addition, we also conduct the zeros of radial solutions in terms of the initial data under specific conditions on K and p. Furthermore, based on the Pohozaev identity and openness for the regions of initial data corresponding to certain types of solutions, we obtain the whole structure of radial solutions depending on various situations.
AB - In this article, we are concerned with the semilinear elliptic equation δu + K(|x|)|u|p-1u = 0 in Rn \ {0}, where n > 2, p > 1, and K(|x|) > 0 in Rn. The correspondence between the initial values of regularly positive radial solutions of the above equation and the associated finite total curvatures will be derived. In addition, we also conduct the zeros of radial solutions in terms of the initial data under specific conditions on K and p. Furthermore, based on the Pohozaev identity and openness for the regions of initial data corresponding to certain types of solutions, we obtain the whole structure of radial solutions depending on various situations.
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U2 - 10.1090/S0002-9947-2011-05192-5
DO - 10.1090/S0002-9947-2011-05192-5
M3 - Article
AN - SCOPUS:79952138358
SN - 0002-9947
VL - 363
SP - 3211
EP - 3231
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 6
ER -