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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.

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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.

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Existence of pseudo almost periodic solutions to some classes of partial hyperbolic evolution equations.

Diagana, Toka (2007)

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

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Existence of positive solutions for $m$ -point boundary value problems on time scales.

Existence of positive solutions for multi-point boundary value problems.

Existence of positive solutions for multipoint boundary value problem with $p$ -Laplacian on time scales.

Existence of positive solutions for nonlocal fourth-order boundary value problem with variable parameter.

Existence of positive solutions for nth-order boundary value problem with sign changing nonlinearity.

Existence of positive solutions for $p$ -Laplacian three-point boundary-value problems on time scales.

Existence of positive solutions for self-adjoint boundary-value problems with integral boundary conditions at resonance.

Existence of positive solutions for semipositone dynamic system on time scales.

Existence of positive solutions for semipositone higher-order BVPS on time scales.

Existence of positive solutions for semi-positone systems.

Existence of positive solutions for singular four-point boundary value problem with a $p$ -Laplacian

Existence of positive solutions for singular fractional differential equations.

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

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