GLOBAL EXISTENCE OF SMALL SOLUTIONS TO SEMILINEAR SCHRODINGER-EQUATIONS

Authors
CHIHARA H
Citation
H. Chihara, GLOBAL EXISTENCE OF SMALL SOLUTIONS TO SEMILINEAR SCHRODINGER-EQUATIONS, Communications in partial differential equations, 21(1-2), 1996, pp. 63-78
Citations number
9
Categorie Soggetti
Mathematics,"Mathematics, Pure",Mathematics,Mathematics
Journal title
Communications in partial differential equations → ACNP
ISSN journal
03605302
Volume
21
Issue
1-2
Year of publication
1996
Pages
63 - 78
Database
ISI
SICI code
0360-5302(1996)21:1-2<63:GEOSST>2.0.ZU;2-W
Abstract
We present global existence theorem for semilinear Schrodinger equatio ns. In general, Schrodinger-type equations do not admit the classical energy estimates. To avoid this difficulty, we use S. Doi's method for Linear Schrodinger-type equations. Combining his method and L(p) - L( q) estimates, we prove the global existence of solutions with small in itial data.