Research On The Existence Of Periodic Positive Solution For Two Kinds Of Differential Equations Based On The Coincidence Degree Theory

Many natural phenomenon and social phenomenon can be described by differential equation. The research of periodic for these phenomena is to study the periodic solutions of these differential equations. Application in practical problems, only the positive solutions are meaningful. So it is particularly important to study the positive periodic solutions. In this paper, coincidence degree theorem and fixed point theorem are used to study the existence of periodic solutions of the p-Laplacian equations and burglary models.Full text main contents are arranged as following:First chapter mainly introduced the research background and research status quo of periodic solution and to preparatory knowledge necessary for this article conclusion, and gives some basic concepts and symbols.The second chapter discussed two kinds of equations of p-Laplace operator of the form with p>1, g:Râ†'R is an arbitrary continuous function, g(t,x):Rx(0,+∞) â†'R is continuous and singular at x=0. By using coincidence degree theory to prove the existence of these two types of equations positive periodic solution. At last, we give the sufficient condition.The third chapter studied two kinds of one-dimensional problem that arises from mathematical modeling for burglary: have at least one positive solution. Where A representing attractiveness for a house to be burglarized, and the burglary density is denoted by N. η describes the rate at which the attractiveness at one site spreads to near-by sites. A0 is the non-dimensional baseline attractiveness value, and A0:[0,L]â†'R be a positive function of class C2. A1 is a constant, and A1(x)>A0(x). We use the fixed point theory and related properties of coincidence degree to prove the existence of positive periodic solutions for the above two kinds of burglary models.