TY  - JOUR
ID  - Hai2019
LB  - Hai2019
AU  - Hai, D. D.
AU  - Wang, X.
TI  - Positive solutions for the one-dimensional p-Laplacian with nonlinear boundary conditions
ST  - Positive solutions for the one-dimensional p-Laplacian with nonlinear boundary conditions
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2019
VL  - 39
IS  - 5
SP  - 675
EP  - 689
DO  - https://doi.org/10.7494/OpMath.2019.39.5.675
UR  - https://doi.org/10.7494/OpMath.2019.39.5.675
AB  - 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.
KW  - \(p\)-Laplacian
KW  - semipositone
KW  - nonlinear boundary conditions
KW  - positive solutions
SN  - 1232-9274
ER  -