Nontrivial Solutions For Asymptotically Autonomous Modified Schr(?)dinger Equation With Asymptotically 3-linear Term

In this thesis,by using Nehari method,Mountain Pass Lemma and Ekeland variational principle,we study the existence of nontrivial solutions for a class of modified Schr(?)dinger equations,where ? ? 0.We make the following assumptions on V,a,g and m:(V0)V? C(R3,R),and inf V(x)>0.(G1)g ? C(R,R),and g is odd.(G3)There exists a constant 0<l<+?,such that(?)(G4)g(t)/t3 ? 0 for t ?0,and t(?)g(t)/t3 is nonincreasing on(-?,0),nondecreasing on(0,+?).(M1)m ? L2(R3),and for all x ? R3,m(x)? 0(m(x)(?)0).And then,as ? = 0,we have the following result:Theorem 1.Assume that(V0)-(Vi),(G1)-(G4)and(A1)hold,then the problem(0.01)has a positive ground state solution.In addition,as a(x)= 1,?>0,we have the following result:Theorem 2.Assume that(V0)-(Vi),(G1)-(G4)and(M1)hold,then there exists a constant ?>0,such that for every ? ?(0,?*),problem(0.01)has at least two nontrivial solutions.