Singular perturbations for third-order nonlinear multi-point boundary value problem
نویسندگان
چکیده
منابع مشابه
Positive Solutions for a Singular Third Order Boundary Value Problem
The existence of positive solutions is shown for the third order boundary value problem, u′′′ = f (x,u),0 < x < 1, u(0) = u(1) = u′′(1) = 0, where f (x,y) is singular at x = 0 , x = 1 , y = 0 , and may be singular at y = ∞. The method involves application of a fixed point theorem for operators that are decreasing with respect to a cone. Mathematics subject classification (2010): 34B16, 34B18.
متن کاملTRIPLE SOLUTIONS FOR NONLINEAR SINGULAR m-POINT BOUNDARY VALUE PROBLEM
In this paper, we study the existence of three solutions to the following nonlinear m-point boundary value problem u′′(t) + βu(t) = h(t)f(t, u(t)), 0 < t < 1, u′(0) = 0, u(1) = m−2 ∑ i=1 αiu(ηi), where 0 < β < π2 , f ∈ C([0, 1] × R ,R). h(t) is allowed to be singular at t = 0 and t = 1. The arguments are based only upon the Leggett-Williams fixed point theorem. We also prove nonexist results.
متن کاملNagumo theorems of third-order singular nonlinear boundary value problems
*Correspondence: [email protected] Institute of Applied Physics and Computational Mathematics, Beijing, 100088, P.R. China College of Mathematics, Jilin University, Changchun, 130012, P.R. China Abstract In this paper, we establish the Nagumo theorems for boundary value problems associated with a class of third-order singular nonlinear equations: (p(t)x′)′′ = f (t, x,p(t)x′, (p(t)x′)′), ∀t ...
متن کاملMultiple Positive Solutions for Nonlinear Singular Third-order Boundary Value Problem in Abstract Spaces
In this paper, we study the nonlinear singular boundary value problem in abstract spaces: { u′′′ + f(t, u) = θ, t ∈ (0, 1), u(0) = u′(0) = θ, u′(1) = ξu′(η), where 0 < η < 1 and 1 < ξ < 1 η , θ denotes the zero element of E, E is a real Banach space, and f(t, u) is allowed to be singular at both end point t = 0 and t = 1. We show the existence of at least two positive solutions of this problem.
متن کاملEigenvalue of boundary value problem for nonlinear singular third-order q-difference equations
In this paper, we establish the existence of positive solutions of a boundary value problem for nonlinear singular third-order q-difference equations Dqu(t) + λa(t)f (u(t)) = 0, t ∈ Iq, u(0) = 0, Dqu(0) = 0, αDqu(1) + βDqu(1) = 0, by using Krasnoselskii’s fixed-point theorem on a cone, where λ is a positive parameter. Finally, we give an example to demonstrate the use of the main result of this...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2005
ISSN: 0022-0396
DOI: 10.1016/j.jde.2005.01.005