Study On The Related Problems Of Positive Radial Solutions For P-Laplacian Problems In Exterior Domains

In recent years,many scholars have studied the existence and uniqueness of positive radial solutions for p-Laplacian problems with boundary conditions in exterior domains.The boundary conditions studied mainly include Dirichlet boundary conditions and other nonlinear boundary conditions.They establish existence and uniqueness results by the method of sub-super solutions,the prior estimates of solutions and the contradiction methods.Therefore,on the basis of the existing literature,we discuss the existence and uniqueness results of positive radial solutions for three types of p-Laplacian problems with Neumann boundary conditions in exterior domains.We prove our results by the method of sub-super solutions,the prior estimates of solutions and the contradiction methods.The specific contents are as follows:The first chapter is the introduction,which briefly introduces the topic selection background,current research status,main work and results of this paper.The second chapter,we study the uniqueness of positive radial solutions for infinite semipositone p-Laplacian problems in exterior domains.Reference [1] gives the existence of the positive radial solutions for a class of infinite semipositone p-Laplacian problems with nonlinear boundary conditions by the method of sub-super solutions.We can also prove that the problem has a positive radial solution by entering its corresponding method.In this chapter,we establish the uniqueness results of positive radial solutions.We prove our results by the prior estimates of solutions and the contradiction methods.The third chapter,we study the uniqueness of positive radial solutions for the singular p-Laplacian problems in exterior domains.Similarly,refer to reference [1] to prove that the problem has a positive radial solution.In this chapter,we establish the uniqueness results of positive radial solutions.We prove our results by the prior estimates of solutions and the contradiction methods.The fourth chapter,we study the existence of positive radial solutions for a class of p-Laplacian problems in exterior domains.In this chapter,we establish the existence results of positive radial solutions.We prove our results by the method of sub-super solutions.The fifth chapter,we summarize and prospect this thesis.