Optimal Controls And Solutions To Several Classes Of Nonlinear Impulsive Differential Equations

This paper is concerned with the optima) control problem of solutions to second-order impulsive differential equations, the solutions are obtained by using a fixed theo-rem of generalized concave operator and a fixed theorem of mixed monotone operator. Also, we consider the existence of solutions to fourth-order differential equations with nonlinear boundary value conditions by using a fixed point theorem of sum operator. Some relevant results are extended and improved.The thesis is divided into four chapters.In chapter1, we introduce the background for the discussed problems of this thesis, and we state the main results concrctely.In chapter2, we study the second-order impulsive integro-differential equations By applying a fixed point theorem of generalized concave operator, we obtain the ex-istence of positive solutions and the optimal control problem of the positive solutions. An example is presented in the end of this chapter to illustrate the application of the obtained results.In chapter3. we discuss the existence of solutions to second-order impulsive differ- ential equation By applying a fixed theorem of mixed monotone operator, we obtain the existence of positive solutions and the optimal control problem of the positive solutions.In chapter4, we consider the existence of solutions to the following fourth-order impulsive differential equation with nonlinear boundary value conditions By using a fixed theorem of sum operator, we discuss the existence and uniqueness of the solution to the fourth-order impulsive differential equation, and extend some of the existing conclusions.