We consider the following third order three-point boundary value problem on a half-line:where η ∈ ( , +∞), but xed, and f : [ , +∞) × ℝ → ℝ satis es Nagumo's condition. We apply Schauder's xed point theorem, the upper and lower solution method, and topological degree theory, to establish existence theory for at least one unbounded solution, and at least three unbounded solutions. To demonstrate the usefulness of our results, we illustrate two examples.Keywords: Three-point boundary value problem, lower and upper solutions, half-line, Schauder's xed point theorem, topological degree theory
MSC: B , B
Let be a periodic time scale in shifts . We use a fixed point theorem due to Krasnosel'skiĭ to show that nonlinear delay in dynamic equations of the form , has a periodic solution in shifts . We extend and unify periodic differential, difference, -difference, and -difference equations and more by a new periodicity concept on time scales.
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