The eigenvalue problem and infinitely many sign-changing solutions for an elliptic equation with critical Hardy constant

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• 作者：Shuying Tian ^{sytian@whut.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Lower bounds of eigenvalues ; Critical Hardy constant ; Infinitely many sign-changing solutions
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：447
• 期：1
• 页码：354-370
• 全文大小：369 K

文摘

By Li–Yau's idea and a more precise Hardy's inequality, we obtain a new lower bound of eigenvalues for an elliptic equation with critical Hardy constant. Then using the lower bounds, we prove that there are infinitely many sign-changing solutions for a class of elliptic equation with critical Hardy constant which extends the results in Schechter and Zou (2005) [9] to the critical Hardy constant case.