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

Chunmei Miao, Junfang Zhao, Weigao Ge (2009)

Czechoslovak Mathematical Journal

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 singular second order boundary value problems.

Guo, Yanping, Gao, Ying, Zhang, Guang (2002)

Applied Mathematics E-Notes [electronic only]

Existence of positive solutions for the symmetry three-point boundary-value problem.

Ma, Qiaozhen (2007)

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

Existence of positive solutions for two nonlinear eigenvalue problems.

Rhouma, Nedra Belhaj, Mâatoug, Lamia (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 discrete elastic beam equation.

Ma, Ruyun, Li, Jiemei, Gao, Chenghua (2010)

Discrete Dynamics in Nature and Society

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 of $n$ -dimensional system of nonlinear differential equations entering into a singular point

Josef Diblík, Miroslava Růžičková (2000)

Archivum Mathematicum

Existence of positive solutions of nonlinear second-order periodic boundary value problems.

Ma, Ruyun, Gao, Chenghua, Chen, Ruipeng (2010)

Boundary Value Problems [electronic only]

Existence of positive solutions of $p$ -Laplacian functional differential equations.

Song, Chang-Xiu (2006)

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

Existence of positive solutions to a boundary value problem for a delayed nonlinear fractional differential system.

Ouyang, Zigen, Chen, Yuming, Zou, Shuliang (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 positive solutions to vector boundary value problems. II.

Ilja Martišovitš (1999)

Mathematica Slovaca

Existence of positive solutions to vector boundary value problems. I.

Ilja Martišovitš (1999)

Mathematica Slovaca

Existence of pseudo-almost automorphic mild solutions to some nonautonomous partial evolution equations.

Diagana, Toka (2011)

Advances in Difference Equations [electronic only]

Existence of quasilinear relaxation shock profiles in systems with characteristic velocities

Guy Métivier, Benjamin Texier, Kevin Zumbrun (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

We revisit the existence problem for shock profiles in quasilinear relaxation systems in the case that the velocity is a characteristic mode, implying that the profile ODE is degenerate. Our result states existence, with sharp rates of decay and distance from the Chapman–Enskog approximation, of small-amplitude quasilinear relaxation shocks. Our method of analysis follows the general approach used by Métivier and Zumbrun in the semilinear case, based on Chapman–Enskog expansion and the macro–micro...

Existence of regularly and rapidly varying solutions for a class of third order nonlinear ordinary differential equations.

Jaroš, Jaroslav, Takaŝi, Kusano, Marić, Vojislav (2006)

Publications de l'Institut Mathématique. Nouvelle Série

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