Article ID Journal Published Year Pages File Type
844920 Nonlinear Analysis: Theory, Methods & Applications 2006 20 Pages PDF
Abstract

Variational methods are used to prove the existence of multiple positive and sign-changing solutions for a Schrödinger equation with singular potential having prescribed finitely many singular points. Some exact local behavior for positive solutions obtained here are also given. The interesting aspects are two. One is that one singular point of the potential V(x)V(x) and one positive solution can produce one sign-changing solution of the problem. The other is that each sign-changing solution changes its sign exactly once.

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Physical Sciences and Engineering Engineering Engineering (General)
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