# Article

 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. .

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