Results in Mathematics

, Volume 44, Issue 3, pp 375-385

First online:

Optimal Existence Conditions for the Periodic Delay ϕ-Laplace Equation with upper and lower Solutions in the Reverse order

  • Wenjie ZuoAffiliated withDept. of Mathematics, Northeast Normal University
  • , Daqing JiangAffiliated withDept. of Mathematics, Northeast Normal University
  • , Donal O’ReganAffiliated withDepartment of Mathematics, National University of Ireland
  • , R. P. AgarwalAffiliated withDepartment of Mathematical Science, Florida Institute of Technology

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In this paper, we show that the monotone iterative technique produces two monotone sequences that converge uniformly to extremal solutions for the periodic delay ϕ-Laplace equation. Moreover, we obtain optimal existence conditions with upper and lower solutions in the reverse order.

Key words and phrases

Existence Upper and lower solutions Monotone iterative technique

MSC 2000