| In this paper,we mainly discuss the existence of nontrivial solutions to two kinds of equations with asymptotically linear.In Chapter 1,according to these problems being discussed in this paper,we give a brief introduction to Schrodinger equations and Kirchhoff type problems of practically significant,domestic and foreign current situation,prerequisites,the full text chapter layout.In Chapter 2,we discuss a kind of Schrodinger equation in (?)N-△u+V(x)u+u = f(u),x∈∟N(0.1)where N ≥3,V(x)decays to zero at infinity,f(t)is asymptotically linear in t at infinity.We prove the existence of one nontrivial solution in H1((?)N)to equation(0.1)by using the Mountain Pass theorem.In Chapter 3,we study a kind of Kirchhoff type problem｛-{a∫∣▽u∣2dx+b}△u+v(x)u=k(x)f(u),x∈(?)3,(2)u∈H1((?)3)where a and b are constants and nonnegative,V(x)and K(x)satisfy corresponding assumptions,∫(t)is asymptotically linear in t at infinity.We prove the existence of one nontrivial solution in H1((?)N)to equation(0.2)by using the Mountain Pass theorem. |
