Sometimes, it’s easy for a computer to predict the future. Simple phenomena, such as how sap flows down a tree trunk, are straightforward and can be captured in a few lines of code using what ...

We prove Hölder regularity results for a class of nonlinear elliptic integro-differential operators with integration kernels whose ellipticity bounds are strongly directionally dependent. These ...

In this paper the estimates for norms of solutions to nonlinear systems are obtained via an integral inequality. As an application we considered affine control systems and systems of equations for ...

We introduce a method for finding general solutions of third-order nonlinear differential equations by extending the modified Prelle-Singer method. We describe a procedure to deduce all the integrals ...

Department of Mathematical Statistics and Differential Equations, Ivan Franko National University of Lviv, Lviv, Ukraine Problems without initial conditions for evolution equations and variational ...

ABSTRACT: In previous papers, we proposed the important Z transformations and obtained general solutions to a large number of linear and quasi-linear partial differential equations for the first time.