Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7222047 | Nonlinear Analysis: Real World Applications | 2018 | 18 Pages |
Abstract
We study the following nonlinear Schrödinger equations in one dimension: (â)âuâ²â²+(1+b(x))u=f(u),uâH1(R),where b(x) satisfies 1+b(x)â¥0, lim|x|ââb(x)=0 and lim¯|x|ââeβ0|x|b(x)â¤0 for β0>2 and f(u) satisfies some properties whose typical example is f(u)=|u|pâ1u (p>1). In this paper, we give conditions of b(x) where (â) has a positive solution and a condition on b(x) where (â) has no nontrivial solutions.
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Authors
Yohei Sato,