Bifurcation of positive entire solutions for a semilinear elliptic equation

Tsing San Hsu*, Huei Li Lin

*Corresponding author for this work

Research output: Contribution to journalJournal Article peer-review

1 Scopus citations


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.

Original languageEnglish
Pages (from-to)349-370
Number of pages22
JournalBulletin of the Australian Mathematical Society
Issue number3
StatePublished - 12 2005


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