논문 해외 국제전문학술지(SCI급) Positive entire solutions of semilinear elliptic equations with quadratically vanishing coefficient
- 학술지 구분 국제전문학술지(SCI급)
- 게재년월 2007-06
- 저자명 배스현
- 학술지명 JOURNAL OF DIFFERENTIAL EQUATIONS
- 발행처명 ACADEMIC PRESS INC ELSEVIER SCIENCE
- 발행국가 해외
- 논문언어 외국어
- 전체저자수 1
홈페이지논문 초록 (Abstract)
We establish that for n >= 3 and p > 1, the elliptic equation Delta u + K(x)u(p) = 0 in R-n possesses a continuum of positive entire solutions with logarithmic decay at 00, provided that a locally Holder continuous function K >= 0 in R-n \ {0}, satisfies K(x) = O(vertical bar x vertica l bar sigma) at x = 0 for some sigma > -2, and vertical bar x vertical b ar(2) K (x) = c + O ([log vertical bar x vertical bar](-theta)) near inf inity for some constants c > 0 and theta > 1. The continuum contains at least countably many solutions among which any two do not intersect. Th is is an affirmative answer to an open question raised in [S. Bae, T.K. Chang, On a class of semilinear elliptic equations in R-n, J. Different ial Equations 185 (2002) 225-250]. The crucial observation is that in th e radial case of K(r) = K(vertical bar x vertical bar I), two fundamenta l weights, (log r)(p-1)(p) and r(n-2)(log r)(-)(p)(p-1) appear in analyz ing the asymptotic behavior of solutions. (C) 2007 Elsevier Inc. All rig hts reserved.