| The boundary value problems of nonlinear equations are research highlights in differential equations.It is of great research value and theoretical meaning to study the existence of solutions of this kind of problems,due to the connection with practical problems in the fields of biological sciences and genetic technology.In this thesis,we study two classes of nonlinear equations,of which the p-Laplacian equation is the extension of the Laplacian equation,which plays a significant role in theory and application.The other is the pendulum equation,which has the strongest practical background in the Duffing equation.In this thesis,the existence and multiplicity of the p-Laplacian equation and the existence of the pendulum equation are studied by using the fixed po:int theorem in cones,the Leggett-Williams fixed point theorem and the principle of least action.Some results in the literature are improved and generalized.This thesis is divided into four parts,the details are as follows:In the first chapter,the research background,research implications and research status of this thesis are briefly reviewed,then the structure of this thesis is briefly summarized.In the second chapter,we study two-part results of the Dirichlet problem for a class of p-Laplacian equation.First,based on the fixed point theorem,we obtain the existence results of at least one nontrivial radially symmetric solutions for the problem and give an example to verify it.Secondly,by using the Leggett-Williams fixed point theorem,we obtain the existence result of at least three or more positive radially solutions for the problem.In the third chapter,we study the pendulum equation with variable damping coefficient Based on the principle of least action,we get the existence result of at least one subharmonic solution of order m of the equation and give the numerical simulation to verify it.In the fourth chapter,we summarize the related work of this thesis.Figure[4]Table[0]Reference[83]... |
PDF Full Text Request