연구홍보포털

논문 초록 (Abstract)

We consider the semilinear elliptic equation Delta u + K (vertical bar x vertical bar)u(P) = 0 in R-N for N > 2 and p > 1, and study separation phenomena of positive radial solutions. With respe ct to intersection and separation, we establisha classification of the solution structures, and investigate the structures of inters ection, partial separation and separation. As a consequence, we obtai n the existence of positive solutions with slow decay when the osci llation of the function r(-l) K (r) with l > -2 around a positive consta nt is small near r = infinity and p is sufficiently large. Moreover , ifthe assumptions hold in the whole space, the equation has the str ucture of separation and possesses a singular solution as theupper lim it of regular solutions. We also reveal that the equation changes i ts nature drastically across a critical exponent pc which is determined by N and the order of the behavior of K (r) as r = vertical bar x vert ical bar -> 0 and infinity. In order to understand how subtle the stru cture is on K at p = pc, we explain the criticality in a similar way a s done by Ding and Ni (1985) [6] for the critical Sobolev exponent p = (N + 2)/(N - 2). (C) 2014 Elsevier Inc. All rights reserved.