The method of lower and upper solutions for fourth order equations with the Navier condition

The method of lower and upper solutions for fourth order equations with the Navier condition

The Method of Lower and Upper Solutions for Some Fourth-order Equations

In this paper, by combining a new maximum principle of fourth-order equations with the theory of eigenline problems, we develop a monotone method in the presence of lower and upper solutions for some fourth-order ordinary differential equation boundary value problem. Our results indicate there is a relation between the existence of solutions of nonlinear fourth-order equation and the first eige...

Differential Equations and the Method of Upper and Lower Solutions

The purpose of this paper is to give an exposition of the method of upper and lower solutions and its usefulness to the study of periodic solutions to differential equations. Some fundamental topics from analysis, such as continuity, differentiation, integration, and uniform convergence, are assumed to be known by the reader. Concepts behind differential equations, initial value problems, and b...

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.

the evaluation of language related engagment and task related engagment with the purpose of investigating the effect of metatalk and task typology

abstract while task-based instruction is considered as the most effective way to learn a language in the related literature, it is oversimplified on various grounds. different variables may affect how students are engaged with not only the language but also with the task itself. the present study was conducted to investigate language and task related engagement on the basis of the task typolog...