| This thesis of Master is composed of four chapters, which mainly studies severalkinds of the second order nolinear differential equations about the oscillatory ofsolutions, and discusses theβ-existence of a kind of general Logistic populationwhich live in a polluted environment with a nonlinear capture. A series of newresults are obtained, and some of them generalized and improved the related resultsin the literature.In Chapter 1 we introduce the background of the problem-researching and themain contents of this paper.The aim of Chapter 2 is to discuss the oscillation of a class of the forced second-order nonlinear nonhomogeneous differential equation (a(t)ψ(b(x(t))k(x'(t)))'+p(t)k(x'(t))+q(t)f(x(t))=r(t),Three new sufficient conditions are given for the oscillation.Chapter 3 is devoted to study the oscillation of a class of second-order nonlineardifferential equations with impulseswhere 0≤t0＜t1＜t2＜…, Some oscillation criteria areobtained.In the last Chapter, theβ-existence of a kind of general Logistic populationwhich live in a polluted environment with a nonlinear capturc x(0)＞0, 0≤C0(0)≤1, 0≤Ce(0)≤1,is discussed. And the sufficient conditions forβ-extinction,β-persistence is stud-ied. The maximal harvesting capacity when the population isβ-persistence is alsoabtained.
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