Positive and negative solutions of one-dimensional beam equation

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• 作者：Pavel Dr&aacute ; bek ^{pdrabek@kma.zcu.cz" class="auth_mail" title="E-mail the corresponding author} ; Gabriela Holubov&aacute ; ; ^{gabriela@kma.zcu.cz" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Fourth order problem ; Beam operator ; Positive solutions ; Negative solutions ; Monotone iterations
• 刊名：Applied Mathematics Letters
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：51
• 期：Complete
• 页码：1-7
• 全文大小：615 K

文摘

In this paper, we show that the usual limitations on the coefficient c=c(x)$c=c\left(x\right)$ in the linear problem u⁽⁴⁾+c(x)u=h(x)$u^{\left(4\right)}+c\left(x\right)u=h\left(x\right)$ with Navier boundary conditions and nonnegative right hand side h$h$ are not necessary to get the existence of positive or negative solutions whenever c(x)$c\left(x\right)$ is a nonconstant function.