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http://dx.doi.org/10.4134/JKMS.2007.44.5.1065

GLOBAL SOLUTIONS OF SEMIRELATIVISTIC HARTREE TYPE EQUATIONS  

Cho, Yong-Geun (Department of Mathematics Pohang University of Science and Technology)
Ozawa, Tohru (Department of Mathematics Hokkaido University)
Publication Information
Journal of the Korean Mathematical Society / v.44, no.5, 2007 , pp. 1065-1078 More about this Journal
Abstract
We consider initial value problems for the semirelativistic Hartree type equations with cubic convolution nonlinearity $F(u)=(V*{\mid}u{\mid}^2)u$. Here V is a sum of two Coulomb type potentials. Under a specified decay condition and a symmetric condition for the potential V we show the global existence and scattering of solutions.
Keywords
semirelativistic Hartree type equations; global existence; scattering; Coulomb type potentials;
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