What is worth pointing out is that in 2 . 1 a class of singularly perturbed second order ordinary differential equations with nonlinear boundary value condi - tions are discussed by using the method of differential inequalities ; in 2 . 2 introduce two small parameters into partial differential equations and obtain the result accordingly ; what ' s more , consider nonlocal problem for ordinary and partial differential equations
12.
In this paper , these two methods are employed to consider three kinds of singular perturbation boundary value problems . in the first section , the existence of solution for a class of non - linear systems with three - point boundary problem is obtained by applying the differential inequality theory . in the second section , we use the differential inequality theory to discuss the non - monotone interior layer solution for one kind of singularly perturbed quasilinear boundary value problems with a turning point . in the third section , the diagonalization method is applied to study the existence of solution for a class of vector differential systems with two - point or three - point boundary problems . meanwhile , the asymptotic estimate of the solution as well as its first - order derivative and its second - order derivative is obtained
13.
The present paper deals with oscillatory properties of solutions for a class of nonlinear impulsive neutral delay parabolic partial differential equations and some new sufficient criteria for oscillation of the equations are obtained under robin and dirichlet boundary value conditions via impulsive neutral differential inequalities of first order
14.
This paper studies the corner layer behavior in quasi linear systems with turning points . under the appropriate conditions and by usin g the theory of differential inequality , the existence of the solution and its c omponentwise uniformly valid asymptotic estimation are obtained when the reduced solution does not have a continuous first - derivative in some point of ( 0 , 1 )
15.
According to the theory of differential inequality and the comparision theorem , we will establish some new and more practical criteria of the extinction , uniform persistence and globally asymptotical stability for partial species of the above system . since the narrate of the main theorem is long , we omit it . to see section 2 of chapter 3 for details
16.
Lyapunov functionals are constructed and employed to obtain sufficient conditions for global asymptotic stability ( gas ) in dependent of the delays . global exponential stability theorems are given by using a method based on delay differential inequality . the method is simple and straightforward in analysis , without resorting to any lyapunov functionals
