| Title:
|
Existence to singular boundary value problems with sign changing nonlinearities using an approximation method approach (English) |
| Author:
|
Lü, Haishen |
| Author:
|
O'Regan, Donal |
| Author:
|
Agarwal, Ravi P. |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
52 |
| Issue:
|
2 |
| Year:
|
2007 |
| Pages:
|
117-135 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
singular boundary value problem |
| Keyword:
|
positive solution |
| Keyword:
|
upper and lower solution |
| MSC:
|
34B15 |
| MSC:
|
34B16 |
| idZBL:
|
Zbl 1164.34351 |
| idMR:
|
MR2305869 |
| DOI:
|
10.1007/s10492-007-0006-5 |
| . |
| Date available:
|
2009-09-22T18:28:51Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134667 |
| . |
| Reference:
|
[1] R. P. Agarwal, D. O’Regan: Singular Differential and Integral Equations with Applications.Kluwer Academic Publishers, Dordrecht, 2003. MR 2011127 |
| Reference:
|
[2] P. Habets, F. Zanolin: Upper and lower solutions for a generalized Emden-Fower equation.J. Math. Anal. Appl. 181 (1994), 684–700. MR 1264540, 10.1006/jmaa.1994.1052 |
| Reference:
|
[3] D. O’Regan: Theory of Singular Boundary Value Problems.World Scientific, Singapore, 1994. MR 1286741 |
| Reference:
|
[4] H. Lü, D. O’Regan, and R. P. Agarwal: An Approximation Approach to Eigenvalue Intervals for Singular Boundary Value Problems with Sign Changing Nonlinearities.to appear. |
| . |
