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 -