Liouville theorems have long been a cornerstone in the study of partial differential equations, offering fundamental insights into the nonexistence of non-trivial solutions under specific growth or ...

We analyze three one parameter families of approximations and show that they are symplectic in Lagrangian sence and can be related to symplectic schemes in Hamiltonian sense by different symplectic ...

The neutral differential equation (1.1) $\frac{{{d^n}}} {{d{t^n}}}[x(t) + h(t)x(t - r)] + \sigma f(t,x(g(t))) = 0$ is considered under the following conditions: n ≥ ...

Ordinary differential equations (ODEs) are also called initial value problems because a time zero value for each first-order differential equation is needed. The following is an example of a ...