標題: EXISTENCE OF POSITIVE NONRADIAL SOLUTIONS FOR NONLINEAR ELLIPTIC-EQUATIONS IN ANNULAR DOMAINS
作者: LIN, SS
交大名義發表
應用數學系
National Chiao Tung University
Department of Applied Mathematics
關鍵字: NONRADIAL SOLUTION;BIFURCATION METHOD;VARIATIONAL METHOD
公開日期: 1-Aug-1992
摘要: We study the existence of positive nonradial solutions of equation DELTA-u + f(u) = 0 in OMEGA(a) , u = 0 on partial derivative-OMEGA(a) , where OMEGA(a) = {x is-an-element-of R(n) : a < x < 1} is an annulus in R(n) , n greater-than-or-equal-to 2 , and f is positive and superlinear at both 0 and infinity . We use a bifurcation method to show that there is a nonradial bifurcation with mode k at a(k) is-an-element-of (0, 1) for any positive integer k if f is subcritical and for large k if f is supercritical. When f is subcritical, then a Nehari-type variational method can be used to prove that there exists a* is-an-element-of (0, 1) such that for any a is-an-element-of (a* , 1) , the equation has a nonradial solution on OMEGA(a) .
URI: http://dx.doi.org/10.2307/2154195
http://hdl.handle.net/11536/3330
ISSN: 0002-9947
DOI: 10.2307/2154195
期刊: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume: 332
Issue: 2
起始頁: 775
結束頁: 791
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