Some qualitative questions on the equation −div(a(x,u,∇u))=f(x, u)

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• 作者：Gaurav Dwivedi ; ^{dwivedi_gaurav@iitgn.ac.in" class="auth_mail" title="E-mail the corresponding author} ; Jagmohan Tyagi ^{jtyagi@iitgn.ac.in" class="auth_mail" title="E-mail the corresponding author jtyagi1@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Picone's identity ; Sturmian comparison theorem ; Monotonicity of the first eigenvalue ; Hardy inequality
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：446
• 期：1
• 页码：456-469
• 全文大小：360 K

文摘

In this article, we establish several applications of Picone's identity for the operator of the form such as Hardy type inequality, Sturmian comparison theorem, monotonicity property of the first eigenvalue, nonexistence of positive supersolutions and Caccioppoli inequality under certain conditions on a.