TY - JOUR
T1 - Structure of the sets of regular and singular radial solutions for a semilinear elliptic equation
AU - Chern, Jann Long
AU - Yanagida, Eiji
PY - 2006/5/15
Y1 - 2006/5/15
N2 - This paper is concerned with the structure of the set of radially symmetric solutions for the equation{A formula is presented}with n > 2. Here the nonlinear term f is assumed to be a smooth function of u that is positive for u > 0 and is equal to 0 for u {less-than or slanted equal to} 0. Then any radial solution u = u ( r ), r = | x |, of the equation is shown to be classified into one of several types according to its behavior as r → 0 and r → ∞. Under the assumption that f is supercritical for small u > 0 and is subcritical for large u > 0, we clarify the entire structure of the set of solutions of various types. The Pohozaev identity plays a crucial role in the investigation of the structure.
AB - This paper is concerned with the structure of the set of radially symmetric solutions for the equation{A formula is presented}with n > 2. Here the nonlinear term f is assumed to be a smooth function of u that is positive for u > 0 and is equal to 0 for u {less-than or slanted equal to} 0. Then any radial solution u = u ( r ), r = | x |, of the equation is shown to be classified into one of several types according to its behavior as r → 0 and r → ∞. Under the assumption that f is supercritical for small u > 0 and is subcritical for large u > 0, we clarify the entire structure of the set of solutions of various types. The Pohozaev identity plays a crucial role in the investigation of the structure.
KW - Elliptic equation
KW - Regular and singular solutions
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U2 - 10.1016/j.jde.2005.08.001
DO - 10.1016/j.jde.2005.08.001
M3 - Letter
AN - SCOPUS:33645975786
VL - 224
SP - 440
EP - 463
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
IS - 2
ER -