Electronic Journal of Qualitative Theory of Differential Equations (Feb 2011)

Upper and lower solutions for BVPs on the half-line with variable coefficient and derivative depending nonlinearity

  • Smail Djebali,
  • S. Zahar

DOI
https://doi.org/10.14232/ejqtde.2011.1.14
Journal volume & issue
Vol. 2011, no. 14
pp. 1 – 18

Abstract

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This paper is concerned with a second-order nonlinear boundary value problem with a derivative depending nonlinearity and posed on the positive half-line. The derivative operator is time dependent. Upon a priori estimates and under a Nagumo growth condition, the Schauder's fixed point theorem combined with the method of upper and lower solutions on unbounded domains are used to prove existence of solutions. A uniqueness theorem is also obtained and some examples of application illustrate the obtained results.