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The stability in terms of two different measures for differential equations with supremum and non-instantaneous impulses is studied using Lyapunov like functions and Razumikhin technique. In these differential equation we have impulses, which start abruptly at some points and their action continue on given finite intervals. An example is given to illustrate the results. [ABSTRACT FROM AUTHOR]

Practical stability for nonlinear differential equations with non-instantaneous impulses and supremum is studied. The impulses start abruptly at some points and their actions continue on given finite intervals. Some sufficient conditions for practical stability and strong practical stability are obtained. An example is given to illustrate some of the results. [ABSTRACT FROM AUTHOR]

The existence of infinitely many weak solutions for the fourth-order differential equation (φ p ( u ″ (t) )) ″ ​ ′ + w (φ p ( u ′ (t) )) ′ + a (t) φ p (u (t)) + b (t) φ q (u (t)) − c (t) φ r (u (t)) = 0 , for t ∈ [0, T] is studied. Here φ p (t) = | t | p − 2 t , 1 < p < q < r , w is a constant, and a, b, c are positive continuous functions on the interval [0, T]. The equation is considered with Dirichlet boundary conditions u (0) = u (T) = u ′ (0) = u ′ (T) = 0. An existence result is proved using the variational method and the symmetric mountain-pass theorem. Some earlier results of [L. Saavedra & S. Tersian, Nonlinear Analysis: Real World Applications 34, (2017), 507–519] and [S. Tersian, Proceedings of 48th Spring Conference of the Union of Mathematicians in Bulgaria, 2019, 27–34] are extended. [ABSTRACT FROM AUTHOR]

We perform new Morawetz identities, interaction Morawetz identities and their corresponding inequalities for the system of N nonlinear defocusing Schrodinger equations (NLS), with N ≥ 2, ... Here, for all ... are coupling parameters, moreover we require that the nonlinearity parameter p is both L²(Rd × T)-supercritical and H¹(Rd × T)-subcritical (or at most H¹(Rd × T)-critical). [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editor discusses various reports presented during the 39th International conference "Applications of Mathematics in Engineering and Economics" held in Sozopol, Bulgaria on June 8-13, 2013 and printed within the issue on topics including differential equations, probability theory, and operations research.