Existence to singular boundary value problems with sign changing nonlinearities using an approximation method approach

Lü, Haishen, O'Regan, Donal, and Agarwal, Ravi P.. "Existence to singular boundary value problems with sign changing nonlinearities using an approximation method approach." Applications of Mathematics 52.2 (2007): 117-135. <http://eudml.org/doc/33280>.

@article{Lü2007,
abstract = {This paper studies the existence of solutions to the singular boundary value problem \[ \left\rbrace \begin\{array\}\{ll\}-u^\{\prime \prime \}=g(t,u)+h(t,u),\quad t\in (0,1) , u(0)=0=u(1), \end\{array\}\right.\] where $g\:(0,1)\times (0,\infty )\rightarrow \mathbb \{R\}$ and $h\:(0,1)\times [0,\infty )\rightarrow [0,\infty )$ are continuous. So our nonlinearity may be singular at $t=0,1$ and $u=0$ and, moreover, may change sign. The approach is based on an approximation method together with the theory of upper and lower solutions.},
author = {Lü, Haishen, O'Regan, Donal, Agarwal, Ravi P.},
journal = {Applications of Mathematics},
keywords = {singular boundary value problem; positive solution; upper and lower solution; singular boundary value problem; positive solution; upper and lower solution},
language = {eng},
number = {2},
pages = {117-135},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence to singular boundary value problems with sign changing nonlinearities using an approximation method approach},
url = {http://eudml.org/doc/33280},
volume = {52},
year = {2007},
}

TY - JOUR
AU - Lü, Haishen
AU - O'Regan, Donal
AU - Agarwal, Ravi P.
TI - Existence to singular boundary value problems with sign changing nonlinearities using an approximation method approach
JO - Applications of Mathematics
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 2
SP - 117
EP - 135
AB - This paper studies the existence of solutions to the singular boundary value problem \[ \left\rbrace \begin{array}{ll}-u^{\prime \prime }=g(t,u)+h(t,u),\quad t\in (0,1) , u(0)=0=u(1), \end{array}\right.\] where $g\:(0,1)\times (0,\infty )\rightarrow \mathbb {R}$ and $h\:(0,1)\times [0,\infty )\rightarrow [0,\infty )$ are continuous. So our nonlinearity may be singular at $t=0,1$ and $u=0$ and, moreover, may change sign. The approach is based on an approximation method together with the theory of upper and lower solutions.
LA - eng
KW - singular boundary value problem; positive solution; upper and lower solution; singular boundary value problem; positive solution; upper and lower solution
UR - http://eudml.org/doc/33280
ER -