科研之友
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摘要
Consider the Schrodinger equation -Delta u = (k + V) u in an infinite slab S = Rn-1 x (0, 1), where V has some type of decay at infinity; three specific types are studied. For each type, we prove necessary conditions for the existence of nontrivial admissible solutions. These conditions involve the norm of V, and the distance of k from the set K = {pi(2)m(2) : m is an element of N}. If V is an element of L-infinity (S) is supported on a set D of finite measure, then these conditions also involve the measure of D, and, in many cases, the inequalities are sharp.
- 出版日期2016-7
