Displaying similar documents to “Positive symmetric solutions of singular semipositone boundary value problems.”

Multiple positive solutions to singular boundary value problems for superlinear second order FDEs

Daqing Jiang (2000)

Annales Polonici Mathematici

Similarity:

We study the existence of positive solutions to the singular boundary value problem for a second-order FDE ⎧ u'' + q(t) f(t,u(w(t))) = 0, for almost all 0 < t < 1, ⎨ u(t) = ξ(t), a ≤ t ≤ 0, ⎩ u(t) = η(t), 1 ≤ t ≤ b, where q(t) may be singular at t = 0 and t = 1, f(t,u) may be superlinear at u = ∞ and singular at u = 0.

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

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

Czechoslovak Mathematical Journal

Similarity:

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.

A class of singular fourth-order boundary value problems with nonhomogeneous nonlinearity

Qingliu Yao (2013)

Annales Polonici Mathematici

Similarity:

We study the existence of positive solutions to a class of singular nonlinear fourth-order boundary value problems in which the nonlinearity may lack homogeneity. By introducing suitable control functions and applying cone expansion and cone compression, we prove three existence theorems. Our main results improve the existence result in [Z. L. Wei, Appl. Math. Comput. 153 (2004), 865-884] where the nonlinearity has a certain homogeneity.

Positive solutions to a singular fourth-order two-point boundary value problem

Qingliu Yao (2011)

Annales Polonici Mathematici

Similarity:

This paper studies the existence of multiple positive solutions to a nonlinear fourth-order two-point boundary value problem, where the nonlinear term may be singular with respect to both time and space variables. In order to estimate the growth of the nonlinear term, we introduce new control functions. By applying the Hammerstein integral equation and the Guo-Krasnosel'skii fixed point theorem of cone expansion-compression type, several local existence theorems are proved.

Positive solutions to nonlinear singular second order boundary value problems

Gabriele Bonanno (1996)

Annales Polonici Mathematici

Similarity:

Existence theorems of positive solutions to a class of singular second order boundary value problems of the form y'' + f(x,y,y') = 0, 0 < x < 1, are established. It is not required that the function (x,y,z) → f(x,y,z) be nonincreasing in y and/or z, as is generally assumed. However, when (x,y,z) → f(x,y,z) is nonincreasing in y and z, some of O'Regan's results [J. Differential Equations 84 (1990), 228-251] are improved. The proofs of the main theorems are based on a fixed point...