Bifurcation of positive entire solutions for a semilinear elliptic equation

Tsing San Hsu*, Huei Li Lin

*此作品的通信作者

研究成果: 期刊稿件文章同行評審

1 引文 斯高帕斯(Scopus)

摘要

In this paper, we consider the nonhomogeneous semilinear elliptic equation (*)λ -△u + u = λK(x)up + h(x) in ℝ N,u ε H1 in (ℝn) where λ ≥ 0, 1 < p < (N + 2)/(N - 2), if N ≥ 3, 1 < p < ∞, if N = 2, h(x) ε H-1(ℝN), 0 ≢ h(x) ≥ 0 in ℝN, K(x) is a positive, bounded and continuous function on ℝN. We prove that if K(x) ≥ K > 0 in ℝN, and lim K(x) = K∞, |x|-∞ then there exists a positive constant λ* such that (*)λ has at least two solutions if λ π (0, λ*) and no solution if λ > λ*. Furthermore, (*)λ has a unique solution for λ = λ* provided that h(x) satisfies some suitable conditions. We also obtain some further properties and bifurcation results of the solutions of (1.1)λ at λ = λ*. Copyright Clearance Centre, Inc.

原文英語
頁(從 - 到)349-370
頁數22
期刊Bulletin of the Australian Mathematical Society
72
發行號3
DOIs
出版狀態已出版 - 12 2005

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