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Fixed points and solutions of boundary value problems at resonance

Tom 115 / 2015

Alaa Almansour, Paul Eloe Annales Polonici Mathematici 115 (2015), 263-274 MSC: Primary 34B15; Secondary 34B27. DOI: 10.4064/ap115-3-5

Streszczenie

We consider a simple boundary value problem at resonance for an ordinary differential equation. We employ a shift argument and construct a regular fixed point operator. In contrast to current applications of coincidence degree, standard fixed point theorems are applied to give sufficient conditions for the existence of solutions. We provide three applications of fixed point theory. They are delicate and an application of the contraction mapping principle is notably missing. We give a partial explanation as to why the contraction mapping principle is not a viable tool for boundary value problems at resonance.

Autorzy

  • Alaa AlmansourDepartment of Mathematics
    University of Dayton
    Dayton, OH 45469-2316, U.S.A.
    e-mail
  • Paul EloeDepartment of Mathematics
    University of Dayton
    Dayton, OH 45469-2316, U.S.A.
    e-mail

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