Boundary value problems involving upper and lower solutions in reverse order

On Second Order Periodic Boundary-value Problems with Upper and Lower Solutions in the Reversed Order

In this paper, we study the differential equation with the periodic boundary value u′′(t) = f(t, u(t), u′(t)), t ∈ [0, 2π] u(0) = u(2π), u′(0) = u′(2π). The existence of solutions to the periodic boundary problem above with appropriate conditions is proved by using an upper and lower solution method.

Periodic Boundary Value Problems and Periodic Solutions of Second Order FDE with Upper and Lower Solutions∗

We use the monotone iterative technique with upper and lower solutions in reversed order to obtain two monotone sequences that converge uniformly to extremal solutions of second order periodic boundary value problems and periodic solutions of functional differential equations(FDEs).

Existence of Extreme Solutions for Fractional Order Boundary Value Problem Using Upper and Lower Solutions Method in Reverse Order

In this paper, we consider the existence of extreme solutions of the boundary value problem for a fractional order differential equation Dδu = f(t, u), t ∈ [0, T ], 0 < δ < 1, 0 < T < ∞, with a nonlinear boundary conditions g(u(0)) = u(T ). Under a lower solution α and un upper solution β with β ≤ α, we establish existence results of extreme solutions by means of the method of upper and lower s...

Upper and Lower Solutions Method for Fourth-order Periodic Boundary Value Problems

The purpose of this paper is to prove the existence of a solution of the following periodic boundary value problem ( u(t) = f(t, u(t), u′′(t)), t ∈ [0, 2π] u(0) = u(2π), u′(0) = u′(2π), u′′(0) = u′′(2π), u′′′(0) = u′′′(2π) in the presence of an upper solution β and a lower solution α with β ≤ α, where f(t, u, v) satisfies one side Lipschitz condition.

Positive Solutions of Sturm-Liouville Boundary Value Problems in Presence of Upper and Lower Solutions