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In this paper we deal with the four-point singular boundary value problem $\{\begin{matrix} {(φ_{p} (u^{'} (t)))}^{'} + q (t) f (t, u (t), u^{'} (t)) = 0, & t \in (0, 1), \\ u^{'} (0) - α u (ξ) = 0, u^{'} (1) + β u (η) = 0, \end{matrix}$ where $φ_{p} (s) = {| s |}^{p - 2} s$ , $p > 1$ , $0 < ξ < η < 1$ , $α, β > 0$ , $q \in C [0, 1]$ , $q (t) > 0$ , $t \in (0, 1)$ , and $f \in C ([0, 1] \times (0, + \infty) \times ℝ, (0, + \infty))$ may be singular at $u = 0$ . By using the well-known theory of the Leray-Schauder degree, sufficient conditions are given for the existence of positive solutions.

Existence of positive solutions for singular fractional differential equations.

Qiu, Tingting, Bai, Zhanbing (2008)

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

Existence of positive solutions for some nonlinear elliptic problems in unbounded domains of $ℝ^{n}$ .

Zeddini, Noureddine (2006)

Abstract and Applied Analysis

Existence of positive solutions for some polyharmonic nonlinear boundary-value problems.

Mâagli, Habib, Toumi, Faten, Zribi, Malek (2003)

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

Existence of positive solutions in generalized boundary value problem for $p$ -Laplacian dynamic equations on time scales.

Zhong, Wenyong, Lin, Wei (2009)

Advances in Difference Equations [electronic only]

Existence of positive solutions of a singular nonlinear boundary value problem.

Ma, Ruyun, Li, Jiemei (2010)

Boundary Value Problems [electronic only]

Existence of positive solutions of fourth-order problems with integral boundary conditions.

Ma, Ruyun, Chen, Tianlan (2011)

Boundary Value Problems [electronic only]

Existence of positive solutions to singular $p$ -Laplacian general Dirichlet boundary value problems with sign changing nonlinearity.

Wei, Qiying, Su, You-Hui, Li, Subei, Yan, Xing-Xue (2009)

Abstract and Applied Analysis

Existence of positive solutions to some impulsive second-order integrodifferential equations.

Atmania, Rahima (2010)

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

Existence of solution and positive solution for a nonlinear third-order $m$ -point BVP.

Sun, Jian-Ping, Jin, Fan-Xia (2010)

Fixed Point Theory and Applications [electronic only]

Existence of solution for third order m-point boundary value problem.

Sun, Jian-Ping, Ren, Qiu-Yan (2010)

Applied Mathematics E-Notes [electronic only]

Existence of solution to nonlinear boundary value problem for ordinary differential equation of the second order in Hilbert space

Eva Rovderová (1992)

Mathematica Bohemica

In this paper we deal with the boundary value problem in the Hilbert space. Existence of a solutions is proved by using the method of lower and upper solutions. It is not necessary to suppose that the homogeneous problem has only the trivial solution. We use some results from functional analysis, especially the fixed-point theorem in the Banach space with a cone (Theorem 4.1, [5]).

Existence of solutions and algorithm for a system of variational inequalities.

Zhao, Yali, Xia, Zunquan, Pang, Liping, Zhang, Liwei (2010)

Fixed Point Theory and Applications [electronic only]

Existence of solutions and nonnegative solutions for prescribed variable exponent mean curvature impulsive system initialized boundary value problems.

Zhi, Guizhen, Zhao, Liang, Chen, Guangxia, Liu, Xiaopin, Zhang, Qihu (2010)

Journal of Inequalities and Applications [electronic only]

Existence of solutions for a certain differential inclusion of third order.

Cernea, A. (2009)

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

Existence of solutions for a class of fourth-order $m$ -point boundary value problems.

Sun, Jian-Ping, Ren, Qiu-Yan (2010)

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

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