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We consider the existence of positive solutions of the equation $1 / λ (t) {(λ (t) φ_{p} (x^{'} (t)))}^{'} + μ f (t, x (t), x^{'} (t)) = 0$ , where $φ_{p} (s) = {| s |}^{p - 2} s$ , p > 1, subject to some singular Sturm-Liouville boundary conditions. Using the Krasnosel’skiĭ fixed point theorem for operators on cones, we prove the existence of positive solutions under some structure conditions.

Positive solutions for second-order singular three-point boundary-value problems with sign-changing nonlinearities.

Ji, Caisheng, Yan, Baoqiang (2010)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Positive solutions for singular discrete boundary value problems.

Cecchi, Mariella, Došlá, Zuzana, Marini, Mauro (2004)

Abstract and Applied Analysis

Positive solutions for singular $m$ -point boundary value problems with sign changing nonlinearities depending on $x^{'}$ .

Ma, Ya, Yan, Baoqiang (2009)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Positive solutions for singular nonlinear beam equation.

Song, Ruhao, Lü, Haishen (2007)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Positive solutions for singular semi-positone Neumann boundary-value problems.

Sun, Yong-Ping, Sun, Yan (2004)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Positive solutions for singular Sturm-Liouville boundary value problems with integral boundary conditions.

Liu, Xiping, Xiao, Yu, Chen, Jianming (2010)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Positive solutions for singular Sturm-Liouville boundary value problems on the half line.

Xu, Jiafa, Yang, Zhilin (2010)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Positive solutions for singular three-point boundary-value problems.

Zhao, Zengqin (2007)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Positive solutions for singular three-point boundary-value problems.

Agarwal, Ravi P., O'Regan, Donal, Yan, Baoqiang (2008)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Positive solutions for singular three-point boundary-value problems with sign changing nonlinearities depending on $x^{'}$ .

Chen, Yun, Yan, Baoqiang, Zhang, Lili (2007)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Positive solutions for singular $φ$ -Laplacian BVPs on the positive half-line.

Djebali, Smaïl, Saifi, Ouiza (2009)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Positive solutions for systems of nonlinear singular differential equations.

Yuan, Yanyan, Zhao, Chenglong, Liu, Yansheng (2008)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Positive solutions for third order multi-point singular boundary value problems

John R. Graef, Lingju Kong, Bo Yang (2010)

Czechoslovak Mathematical Journal

We study a third order singular boundary value problem with multi-point boundary conditions. Sufficient conditions are obtained for the existence of positive solutions of the problem. Recent results in the literature are significantly extended and improved. Our analysis is mainly based on a nonlinear alternative of Leray-Schauder.

Positive solutions of a singular positone and semipositone boundary value problems for fourth-order difference equations.

Yuan, Chengjun (2010)

Discrete Dynamics in Nature and Society

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