Shock Layer Behavior for Vector Boundary Value Problems and Kinks in the Lower and Upper Solutions

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

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).

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.

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.

Existence of multiple solutions for Sturm-Liouville boundary value problems

In this paper, based on variational methods and critical point theory, we guarantee the existence of infinitely many classical solutions for a two-point boundary value problem with fourth-order Sturm-Liouville equation; Some recent results are improved and by presenting one example, we ensure the applicability of our results.