Existence of positive nonradial solutions for nonlinear elliptic equations in annular domains

Song-Sun Lin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

We study the existence of positive nonradial solutions of equation Δu + f(u) = 0 in Ωa , u = 0 on ∂Ωa, where Ωa= x ϵ ℛn : a < x < 1 is an annulus in R , n ≥ 2 , and f is positive and superlinear at both 0 and ∞ . We use a bifurcation method to show that there is a nonradial bifurcation with mode k at ak ϵ (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 ϵ (0, 1) such that for any a ϵ a , 1, the equation has a nonradial solution on Ωa .

Original languageEnglish
Pages (from-to)775-791
Number of pages17
JournalTransactions of the American Mathematical Society
Volume332
Issue number2
DOIs
StatePublished - 1 Jan 1992

Keywords

  • Bifurcation method
  • Nonradial solution
  • Variational method

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