An identity for a quasilinear ODE and its applications to the uniqueness of solutions of BVPs

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9 Citations (Scopus)

Abstract

The following boundary value problem(1.1)(φp (u)) + a (x) f (u) = 0, x0 < x < x1,(1.2)u (x0) = u (x1) = 0, is considered, where φp (s) = | s |p - 2 s, p > 1, a ∈ C1 [x0, x1], a (x) > 0 for x ∈ [x0, x1], and f ∈ C1 (R). An identity for solutions of (1.1) and its linearized equation is derived. Some applications of the identity to uniqueness of solutions of problem (1.1)-(1.2) are presented. Non-uniqueness examples for problem (1.1)-(1.2) are also established. Moreover the results obtained here are applied to the study of radially symmetric solutions of the Dirichlet problem for elliptic equations in annular domains.

Original languageEnglish
Pages (from-to)206-217
Number of pages12
JournalJournal of Mathematical Analysis and Applications
Volume351
Issue number1
DOIs
Publication statusPublished - 2009 Mar 1
Externally publishedYes

Keywords

  • Quasilinear equation
  • Two-point boundary value problem
  • Uniqueness

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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