Integral Estimates And Liouville Type Theorems Of Nonnegative Solutions For A Class Of Degenerate Elliptic Equations

This thesis is maily based on the truncation function technique,energy method and the basis of partial differential equations,the nonexistence of positive solutions for a class of degenerate elliptic equations with Grushin operators on R^N=R×R^m(m>2) is studied.It is composed of five chapters.In Chapter 1,we briefly introduce the research background and the present situation at home and abroad of Liouville type theorems for nonnegative solutions of Elliptic Equa-tions and Grushin operator,and gives some lemmas to be used in the proof of theorems in the following chapters.In Chapter 2,we use the knowledge of Green formula,divergence theorem and Young inequality to calculate and nonlinear energy estimate the equations,the integral estimates of postive solutions for a class degenerate elliptic equations are obtained and the Liouville type theorems of nonnegative solutions for degenerate elliptic equations are proved.In Chapter 3,by using the methods similar to those in Chapter 2,generalizes the nonexistence result of positive solutions for degenerate elliptic equations,establishes the integral estimates and Liouville type theorems of nonnegative solutions for weighted de-generate elliptic equations.In Chapter 4,by using the methods similar to those in Chapter 2 and Chapter 3,and the integral estimates and the Liouville type theorems of nonnegative solutions for nonlinear degenerate elliptic equations are established.In the last Chapter,summarizes and looks forward to the main work of this paper,and puts forward some points to be improved.