AN ASYMPTOTICALLY PERIODIC SCHRÖDINGER EQUATION WITH INDEFINITE LINEAR PART
AN ASYMPTOTICALLY PERIODIC SCHRÖDINGER EQUATION WITH INDEFINITE LINEAR PART
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DOI：
10.1142/s0219199702000853
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发表时间：
2002-11
影响因子：
1.6
通讯作者：
Gongbao Li;A. Szulkin
中科院分区：
文献类型：
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作者：
Gongbao Li;A. Szulkin
我们考虑薛定谔方程- Δ u + V(x)u = f(x,u)，其中V是周期的，f在x变量中是渐近周期的，0在- Δ + V的谱隙中，f为渐近线性或超线性，为|u|→∞。我们证明了这个方程有一个解u∈H1 (RN), u≠0。
We consider the Schrodinger equation - Δ u + V(x)u = f(x,u), where V is periodic and f asymptotically periodic in the x-variables, 0 is in a spectral gap of - Δ + V and f is either asymptotically linear or superlinear as |u| → ∞. We show that this equation has a solution u ∈ H1 (RN), u ≠ 0.