Asymptotic behaviour of the solutions of a certain type of the third order differential equations
This paper is concerned with the problem of asymptotic equivalence for positive rapidly decaying solutions of a class of second order quasilinear ordinary differential equations. Its application to exterior Dirichlet problems is also given.
Asymptotic estimates of solutions and their derivatives for n-th order nonhomogeneous ODEs with constant coefficients are obtained, provided the associated characteristic polynomial is (asymptotically) stable. Assuming, additionally, the stability of the so called "shifted polynomials" (see below) to the characteristic one, the estimates can be still improved.
Asymptotic forms of solutions of half-linear ordinary differential equation are investigated under a smallness condition and some signum conditions on . When , our results reduce to well-known ones for linear ordinary differential equations.
In this paper we deal with the problem of asymptotic integration of nonlinear differential equations with Laplacian, where . We prove sufficient conditions under which all solutions of an equation from this class are converging to a linear function as .