On the number of radially symmetric solutions to dirichlet problems with jumping nonlinearities of superlinear order

Alfonso Castro, Hendrik J. Kuiper

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

This paper is concerned with the multiplicity of radially symmetric solutions u(x) to the Dirichlet problem Δu + f(u) = h(x) + cφ(x) on the unit ball Ω ⊃ RN with boundary condition u = 0 on ∂ω. Here 0(x) is a positive function and /(u) is a function that is superlinear (but of subcritical growth) for large positive u, while for large negative u we have that f'(u) < n, where p, is the smallest positive eigenvalue for Δ1 + μ = 0 in ω with -0 on ∂ω. It is shown that, given any integer k > 0, the value c may be chosen so large that there are 2k + 1 solutions with k or less interior nodes. Existence of positive solutions is excluded for large enough values of c.

Original languageEnglish (US)
Pages (from-to)1919-1945
Number of pages27
JournalTransactions of the American Mathematical Society
Volume351
Issue number5
DOIs
StatePublished - 1999

Keywords

  • Critical exponent
  • Dirichlet problem
  • Nodal curves
  • Radially symmetric
  • Superlinear jumping nonlinearity

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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