Existence And Multiplicity Of Solutions For Two Classes Of Nonlinear Boundary Value Problems With P-laplace Operators

With the increasing update of science and technology,nonlinear differential equa-tions have always attracted people's attention.It is not only an important branch in the field of mathematics,but also has a pivotal position in many disciplines such as physics,chemistry,and biology.The existence and multiplicity of solutions have always been hot issues in the study of nonlinear differential equations.In this paper,by using the variational method and the monotone iterative technique,we studied the existence and multiplicity of solutions for a class of fourth-order p-Laplacian impulsive differential equation boundary value problems and a class of nonlinear multi-parameter weight-ed singular p-Laplacian Lane-Emden systems,respectively.According to the research content and methods,this paper is divided into four chapters.The first chapter summarizes the background of nonlinear boundary value prob-lems and Lane-Emden systems,and the current research status of these two classes of problems.Briefly introduces the structure and main results of this paper.The second chapter studied the existence and multiplicity of solutions for a class of fourth-order impulsive boundary value problems with p-Laplace operator and nonlinear boundary conditions.By defining the corresponding functional,using the variational method and the mountain pass lemma,and the mountain pass lemma in the symmetric form,we obtained the existence and multiplicity of the solution for the above problem.The third chapter studies a class of nonlinear multi-parameter weighted Lane-Emden systems with singularity and p-Laplace operator.Using the monotonic iterative technique,the existence and upper and lower bounds estimate of the extremal curve for the Lane-Emden system are obtained.At the same time,the relationship between the order of the solution and the order of the parameters is proved.In the fourth chapter,we give a summary of the paper.