@Article{Hai2019,
author = "Hai, D. D. and Wang, X.",
title = "Positive solutions for the one-dimensional p-Laplacian with nonlinear boundary conditions",
journal = "Opuscula Math.",
year = "2019",
volume = "39",
number = "5",
pages = "675--689",
doi = "https://doi.org/10.7494/OpMath.2019.39.5.675",
url = "https://doi.org/10.7494/OpMath.2019.39.5.675",
abstract = "We prove the existence of positive solutions for the \(p\)-Laplacian problem \[\begin{cases}-(r(t)\phi (u^{\prime }))^{\prime }=\lambda g(t)f(u),& t\in (0,1),\\au(0)-H_{1}(u^{\prime }(0))=0,\\cu(1)+H_{2}(u^{\prime}(1))=0,\end{cases}\] where \(\phi (s)=|s|^{p-2}s\), \(p\gt 1\), \(H_{i}:\mathbb{R}\rightarrow\mathbb{R}\) can be nonlinear, \(i=1,2\), \(f:(0,\infty )\rightarrow \mathbb{R}\) is \(p\)-superlinear or \(p\)-sublinear at \(\infty\) and is allowed be singular \((\pm\infty)\) at \(0\), and \(\lambda\) is a positive parameter.",
keywords = "\(p\)-Laplacian, semipositone, nonlinear boundary conditions, positive solutions",
issn = "1232-9274"
}