论文标题
有界对称域中加权椭圆超线问题的非放置溶液
Nonradial solutions of weighted elliptic superlinear problems in bounded symmetric domains
论文作者
论文摘要
目前的工作有两个目标。首先，我们证明了一个重量\ - 超级椭圆形问题在单位球中具有无限的许多非放射溶液。其次，我们在Annuli中获得相同的结论，以涉及重量的更一般的非线性。我们在域内使用$ k-1 $零的径向溶液的能量水平和简单计数的估计值。由于田中\ cite [2008] {tanaka1}和\ cite [2007] {tanaka2}引起的独特结果非常有用。
The present work has two objectives. First, we prove that a weight\-ed superlinear elliptic problem has infinitely many nonradial solutions in the unit ball. Second, we obtain the same conclusion in annuli for a more general nonlinearity which also involves a weight. We use a lower estimate of the energy level of radial solutions with $k-1$ zeros in the interior of the domain and a simple counting. Uniqueness results due to Tanaka \cite[2008]{Tanaka1} and \cite[2007]{Tanaka2} are very useful in our approach.
