Existence of Solutions for a Nonlocal Boundary Value Problem at Resonance on the Half-Line

  • S. Djafri
  • T. MoussaouiEmail author
  • D. O’Regan
Original Research


In this paper we are interested in the existence of solutions for the following boundary value problem at resonance on the half-line
where \(f:\mathbb {R}^{+}\times \mathbb {R}^{2}\rightarrow \mathbb {R}\) is q-Carathéodory, \( g:\mathbb {R}^{+}\rightarrow \mathbb {R}^{+} \) is a nondecreasing function with \(g(0)=0\) under the resonance condition \(g(\infty )= 1\). The coincidence degree theory of Mawhin [17] is used to establish the existence of at least one solution for the posed problem.


Coincidence degree Boundary value problem Resonance Unbounded interval 

Mathematics Subject Classification

34B10 34B15 34B45 70K30 



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Copyright information

© Foundation for Scientific Research and Technological Innovation 2019

Authors and Affiliations

  1. 1.University of Sciences and Technology Houari BoumedienneBab EzzouarAlgeria
  2. 2.Laboratory of Fixed Point Theory and ApplicationsÉcole Normale SupérieureKoubaAlgeria
  3. 3.School of Mathematics, Statistics and Applied MathematicsNational University of IrelandGalwayIreland

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