In this note we prove some variants of Lagrange’s mean value theorem. The main tools to prove these results are some elementary auxiliary functions.

In this note we prove some variants of Lagrange’s mean value theorem. The main tools to prove these results are some elementary auxiliary functions.

This note deals with some variants of Wayment’s Mean Value Theorem for integrals. Our approach is rather elementary and does not use advanced techniques from analysis. The simple auxiliary functions were used to prove the results.

In this paper we study the existence and uniqueness of the weak solution of a mathematical model that describes the vibration of a string. This model is given by a wave equation with dynamic boundary conditions. Also, we show that this model is conservative but is not exponentially stable.

In this paper we study the existence and uniqueness of the weak solution of a mathematical model that describes the vibration of a string. This model is given by a wave equation with dynamic boundary conditions. Also, we show that this model is conservative but is not exponentially stable.