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Global Results for Solution to the Mass-Critical Schrödinger Equation with Convolution Nonlinearity in R^n
Mathematics and Education in Mathematics, Tome 39 (2010) no. 1, pp. 162-168 Cet article a éte moissonné depuis la source Bulgarian Digital Mathematics Library

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We are concerned with a class of L^2 - critical nonlinear Schrödinger equations in R^(1+n) with convolution nonlinearity of Hartree type. We aim to establish local and global existence and well-posedness of solutions in a small neighborhood of the origin in L^2 (R^n). As a natural consequence of the global results, we prove the existence of scattering operator for small initial data. *2000 Mathematics Subject Classification: 35A05, 35Q55.
Keywords: Nonlinear Schrödinger Equation, Convolution Nonlinearity, Critical Mass, Local and Global Existence, Scattering 
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Venkov, George; Genev, Hristo. Global Results for Solution to the Mass-Critical Schrödinger Equation with Convolution Nonlinearity in R^n. Mathematics and Education in Mathematics, Tome 39 (2010) no. 1, pp. 162-168. http://geodesic.mathdoc.fr/item/MEM_2010_39_1_a15/