The Theory Of Differential Inequalities And Its Application To Singularly Perturbed Nonlinear Boundary Value Problems

In this dissertation, we discuss the existence of solutions and the asymptotic behavior of solutions for several classes singularly perturbed nonlinear boundary value problems systematically by using the theories of differential inequalities.The application of singularly perturbed problems is very wide and aroused scholars' attention in world , the theories of differential inequalities became an important means to deal with singularly perturbed nonlinear boundary value problems, which feature is: it can prove the existence of solutions and obtain the precise estimate of solution; using the theories of differential inequalities, we can simply and effectively obtain the results of using other solutions and can deal with more complicated problems. We have found the solution is very useful in different applied fields, it will be seen that for the general classes of problems which we study in the dissertation, this inequality technique leads elegantly(and easily) to some fairly general results about existence of solutions and their asymptotic beaver. Many results which have been obtained over the years by a variety of methods can now be obtained by this method, which we hope will also very clearly reveal the fundamental asymptotic processes at work.In this dissertation, First, we proved the existence of solutions for Dirichlet boundary value problems using the upper and lower method, then study the existence of solutions for singularly perturbed nonlinear equation and obtained some important differential inequalities theorems. Secondly, we discuss the existence of solutions and the asymptotic behavior of...