Mean value theorem for boundary value problems with given 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).

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.

Existence of positive solutions for fourth-order boundary value problems with three- point boundary conditions

In this work, by employing the Krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime pri...

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

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.