This paper focuses on the mathematical study of the existence of solitary gravity waves (solitons) and their characteristics (amplitude, velocity, [Formula: see text]) generated by a piston wave maker lying upstream of a horizontal channel. The mathematical model requires both incompressibility condition, irrotational flow of no viscous fluid and Lagrange coordinates. By using both the inverse ...

We consider a singular Sturm-Liouville expression with the indefinite weight sgnx. To this expression there is naturally a self-adjoint operator in some Krein space associated. We characterize the local definitizability of this operator in a neighbourhood of ∞. Moreover, in this situation, the point ∞ is a regular critical point. We construct an operator A = (sgnx)(−d2/dx2 + q) with non-real sp...

Using the fixed point theorem in partially ordered sets, we obtain sufficient conditions for existence of a unique positive solution to boundary-value problem Sturm-Liouville type nonlinear ordinary differential equation, and give an example illustrating results obtained.

The purpose of this study is to examine the properties scattering solutions and function an impulsive Sturm-Liouville boundary value problem on semi axis. By using Jost solutions, we obtain function, asymptotic representation resolvent operator. Finally, unperturbated equation.