Solutions Of Several Nonlinear Equations

In this paper, we have mainly studied some solution problems of nonlinear opera-tor equations. We have obtained the existence result for unbounded connected compo-nent of solutions set of some nonlinear operator equations with parameter by using theglobal bifurcation theories, and then obtained some existence results for positive solu-tions of some non-positive operator equations by using the positive connected propertyof the operators.We also have studied solutions of impulsive equation by using the na-ture of fixed point index and upper and lower solution method.The first chapter introduces concisely the historical situation, the development andthe research background as well as the main results done in this paper.In Chapter2, we have given the existence of positive solutions of non-linear oper-ator equations under linear conditions and its application.In Chapter3, we have given the existence of positive solutions of non-linear oper-ator equations under ultra linear conditions and its application.In Chapter4, we studied the sign-changing solution, positive solution and negativesolution of two point boundary value problem of impulsive equation by using the natureof fixed point index and upper and lower solution method.