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 λ ≥ 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 λ = 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,λ>0,we have the following result:Theorem 2.Assume that(V0)-(Vi),(G1)-(G4)and(M1)hold,then there exists a constant λ>0,such that for every λ ∈(0,λ*),problem(0.01)has at least two nontrivial solutions.