Global extstence of small solutions to semiliner schrödinger equations

Abstract

We present global existence theorem for semilinear schrödinger equations. In general, Schrödinger-type equations do not admit the classical energy estimates. To avoid this difficulty, we use S. Doi's method for linear Schrödinger-type equations. Combining his method and L^p-L^q estimates, we prove the global existence of solutions with small initial data.

^∗Present address: Department of Mathematical Sciences. Shinshu University, Matsumoto 390. JAP.4N

^∗Present address: Department of Mathematical Sciences. Shinshu University, Matsumoto 390. JAP.4N

Notes

^∗Present address: Department of Mathematical Sciences. Shinshu University, Matsumoto 390. JAP.4N