Homoclinic Solutions Of The Second Order Impulsive Differential Equations And Boundary Value Problem

This thesis is concerned with the existence of weak solutions for second order boundary value problem for impulsive dynamic equations on time scales,and the ex-istence of nontrivial homoclinic solutions for second-order differential equations with impulses.Main results are as follows:1.Under super-linearity.Ambrosetti-Rabinowitz condition and some nonlinear impulsive perturbation,we prove the existence of weak solutions of the following sec-ond order boundary value problem for impulsive dynamic equations on time scales by using Mountain Pass Lemma: where T is a Time Scale,[0,T]T:=[0,T]∩T,σ(0)=0 andσ(T)=T.f:[0,T]T×Râ†'R,Ij∈C[R,R].{Aj},{Bj}are real sequences which satisfy:Bj=(1+ Aj)â†'-1 and∑k=1 p|Ak|<1,the impulsive points tj∈[0,T]T are all right-dense,and 0=to