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Positive and maximal positive solutions of singular mixed boundary value problem

Ravi Agarwal, Donal O’Regan, Svatoslav Staněk (2009)

Open Mathematics

The paper is concerned with existence results for positive solutions and maximal positive solutions of singular mixed boundary value problems. Nonlinearities h(t;x;y) in differential equations admit a time singularity at t=0 and/or at t=T and a strong singularity at x=0.

Positive and monotone solutions of an $m$ -point boundary-value problem.

Palamides, Panos K. (2002)

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

Positive periodic solutions for Liénard type $p$ -Laplacian equations.

Meng, Junxia (2009)

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

Positive solution of singular boundary value problem for a nonlinear fractional differential equation.

Wang, Changyou, Wang, Ruifang, Wang, Shu, Yang, Chunde (2011)

Boundary Value Problems [electronic only]

Positive solution to a singular $(k, n - k)$ conjugate boundary value problem

Qingliu Yao (2011)

Mathematica Bohemica

Positive solution to a singular $p$ -Laplacian BVP with sign-changing nonlinearity involving derivative on time scales.

Su, You-Hui, Li, Subei, Huang, Can-Yun (2009)

Advances in Difference Equations [electronic only]

Positive solution to nonzero boundary values problem for a coupled system of nonlinear fractional differential equations.

Wang, Jinhua, Xiang, Hongjun, Liu, Zhigang (2010)

International Journal of Differential Equations

Positive solutions and continuous branches for boundary-value problems of differential inclusions.

Hoai, Nguyen Thi, Loi, Nguyen Van (2007)

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

Positive solutions and eigenvalue intervals of a nonlinear singular fourth-order boundary value problem

Qingliu Yao (2013)

Applications of Mathematics

We consider the classical nonlinear fourth-order two-point boundary value problem $\{\begin{matrix} u^{(4)} (t) = λ h (t) f (t, u (t), u^{'} (t), u^{''} (t)), 0 < t < 1, \\ u (0) = u^{'} (1) = u^{''} (0) = u^{'''} (1) = 0 . \end{matrix}$ In this problem, the nonlinear term $h (t) f (t, u (t), u^{'} (t), u^{''} (t))$ contains the first and second derivatives of the unknown function, and the function $h (t) f (t, x, y, z)$ may be singular at $t = 0$ , $t = 1$ and at $x = 0$ , $y = 0$ , $z = 0$ . By introducing suitable height functions and applying the fixed point theorem on the cone, we establish several local existence theorems on positive solutions and obtain the corresponding eigenvalue intervals.

Positive solutions and eigenvalue intervals of a singular third-order boundary value problem

Qingliu Yao (2011)

Annales Polonici Mathematici

This paper studies positive solutions and eigenvalue intervals of a nonlinear third-order two-point boundary value problem. The nonlinear term is allowed to be singular with respect to both the time and space variables. By constructing a proper cone and applying the Guo-Krasnosel'skii fixed point theorem, the eigenvalue intervals for which there exist one, two, three or infinitely many positive solutions are obtained.