## Abstract and Applied Analysis

### Positive Solutions for Second-Order Singular Semipositone Differential Equations Involving Stieltjes Integral Conditions

#### Abstract

By means of the fixed point theory in cones, we investigate the existence of positive solutions for the following second-order singular differential equations with a negatively perturbed term: $-{u}^{\prime \prime }(t)=\lambda [f(t,u(t))-q(t)]$, $0, $\alpha u(0)-\beta {u}^{\prime }(0)={\int }_{0}^{1}u(s)d\xi (s)$, $\gamma u(1)+\delta {u}^{\prime }(1)={\int }_{0}^{1}u(s)d\eta (s),$where $\lambda >0$ is a parameter; $f:(0,1)×(0,\infty )\to [0,\infty )$ is continuous; $f(t,x)$ may be singular at $t=0$, $t=1,$ and $x=0$, and the perturbed term $q:(0,1)\to [0,+\infty )$ is Lebesgue integrable and may have finitely many singularities in $(0,1)$, which implies that the nonlinear term may change sign.

#### Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 696283, 21 pages.

Dates
First available in Project Euclid: 4 April 2013

https://projecteuclid.org/euclid.aaa/1365099937

Digital Object Identifier
doi:10.1155/2012/696283

Mathematical Reviews number (MathSciNet)
MR2947680

Zentralblatt MATH identifier
1251.34040

#### Citation

Jiang, Jiqiang; Liu, Lishan; Wu, Yonghong. Positive Solutions for Second-Order Singular Semipositone Differential Equations Involving Stieltjes Integral Conditions. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 696283, 21 pages. doi:10.1155/2012/696283. https://projecteuclid.org/euclid.aaa/1365099937

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