For the third order differential equation, y′′′ = f(x, y, y′, y′′), we consider uniqueness implies existence results for solutions satisfying the nonlocal 4-point boundary conditions, y(x1) = y1, y(x2) = y2, y(x3)− y(x4) = y3. Uniqueness of solutions of such boundary value problems is intimately related to solutions of the third order equation satisfying certain nonlocal 3-point boundary condit...

This paper studies nonlinear wave propagation in a bubble-liquid mixture based on the third-order Kudryashov–Sinelshchikov (KS) equation. Symmetry is classified and reduced through symmetry group method. Through generalized conditional method, this equation classified, considered are second, third, fourth, fifth-order, respectively. Meanwhile, equations transformed into system of ordinary diffe...

With the development of modern society, research on properties of ordinary differential equation is becoming one of the hotspots in mathematical field. Neutral differential equation which is usually generated in natural science and engineering field is always extensively concerned by many scientific researchers for it can effectively describe multiple complex phenomena in natural world. In rece...

We study the linearization of a class of Liénard type nonlinear second-order ordinary differential equations from the generalized Sundman transformation viewpoint. The linearizing generalized Sundman transformation for the class of equations is constructed. The transformation is used to map the underlying class of equations into a linear second-order ordinary differential equation which is not ...