Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7222578 | Nonlinear Analysis: Theory, Methods & Applications | 2018 | 24 Pages |
Abstract
We consider the Cauchy problem for nonlinear Schrödinger equations in a general domain ΩâRN. Construction of solutions has been only done by classical compactness method in previous results. Here, we construct solutions by a simple alternative approach. More precisely, solutions are constructed by proving that approximate solutions form a Cauchy sequence in some Banach space. We discuss three different types of nonlinearities: power type nonlinearities, logarithmic nonlinearities and damping nonlinearities.
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Authors
Masayuki Hayashi,