| In the present thesis, we consider the Cauchy problem of the following nonlinear nonelliptic Schrodinger equationswhere K(t,x) is a given real-valued function, t ∈ R, x ∈ Rn, n ≥ 2,0 < α < 4/n, ∈j ∈G {-1,1}, 1 ≤ j ≤ n,i = (-1)1/2. Let φ0 ∈ Hs(Rn) (usual Sobolev space) where 0 ≤ s ≤ 1. The unknown u{t, x) is a complex-valued function of real variables t and x, simply denoted by u(t).The thesis is divided into three chapters. The frist chapter is the introduction. In Section 1 of the chapter, the physical background of Schrodinger equations is briefly described and main results of the thesis are presented.In the second chapter, we obtain estimates of the nonlinearity of the equations and prove the exsitence of the unique local-in-time solutions of the equations in Lebesgue space of Lq(It, Lr(Rn)) or Besov space of Lq(It, Bsr,2(Rn)) corresponding to the initial data φ0 ∈ L2(Rn) or φ0∈ Hs(Rn) by Strichartz' inequality and the contraction mapping principle. Here 0 < s < 1,(q,r) is an admissible pair. In addition, Remark 2.2 shows that the equations admit global solutions in Lebesgue space of Lq(R, Lr(Rn)) corresponding to small initial data in L2(Rn) when α = 4/n.In the last chapter, by L2-conservation law of u(t), we prove the main results of the present thesis, i.e.,exsitence of global solutions of the equations. Finally, we consider a nonelliptic Schrodinger system, arising in studying of condensed material for which similar results are obtained.
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