Global preservation of nodal structure in coupled systems of nonlinear sturm-liouville boundary value problems

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Abstract

In this paper, we examine the solution set to the coupled system where λ, μ∈ R, x∈ [a, b], and the system (*) is subject to zero Dirichlet boundary data on u and v. We determine conditions on f and g which permit us to assert the existence of continua of solutions to (*) characterized by u having n−1 simple zeros in (a, b), v having m− 1 simple zeros in (a, b), where n and m are positive but not necessarily equal integers. Moreover, we also determine conditions under which these continua link solutions to (*) of the form (λ,μ, u, 0) with u having n− 1 simple zeros in (a, b) to solutions of (*) of the form (λ,μ, 0, v) with v having m−1 simple zeros in (a, b).

Original languageEnglish (US)
Pages (from-to)633-644
Number of pages12
JournalProceedings of the American Mathematical Society
Volume107
Issue number3
DOIs
StatePublished - 1989

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ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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