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A system of Volterra integral equations with blowing up solutions

Volume 146 / 2017

Wojciech Mydlarczyk Colloquium Mathematicum 146 (2017), 99-110 MSC: Primary 45G15; Secondary 45D05, 45M20. DOI: 10.4064/cm6842-1-2016 Published online: 26 August 2016


A system of nonlinear integral equations related to combustion problems is considered. Necessary and sufficient conditions for the existence and explosion of positive solutions are given. Also the uniqueness of positive solutions is shown. The main results are obtained by monotonicity methods.


  • Wojciech MydlarczykFaculty of Pure and Applied Mathematics
    Hugo Steinhaus Center
    Wrocław University of Science and Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland

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