Article ID Journal Published Year Pages File Type
7222047 Nonlinear Analysis: Real World Applications 2018 18 Pages PDF
Abstract
We study the following nonlinear Schrödinger equations in one dimension: (∗)−u′′+(1+b(x))u=f(u),u∈H1(R),where b(x) satisfies 1+b(x)≥0, lim|x|→∞b(x)=0 and lim¯|x|→∞eβ0|x|b(x)≤0 for β0>2 and f(u) satisfies some properties whose typical example is f(u)=|u|p−1u (p>1). In this paper, we give conditions of b(x) where (∗) has a positive solution and a condition on b(x) where (∗) has no nontrivial solutions.
Related Topics
Physical Sciences and Engineering Engineering Engineering (General)
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