On a Singular Second-Order Multipoint Boundary Value Problem at Resonance
نویسندگان
چکیده
منابع مشابه
Nontrivial Solutions of Singular Second Order There-point Boundary Value Problem at Resonance
The singular second order three-point boundary value problem at resonance { x′′(t) = f(t, x(t)), 0 < t < 1, x′(0) = 0, x(η) = x(1), are considered under some conditions concerning the first eigenvalues corresponding to the relevant linear operators, where η ∈ (0, 1) is a constant, f is allowed to be singular at both t = 0 and t = 1. The existence results of nontrivial solutions are given by mea...
متن کاملPositive Solutions to a Singular Second Order Boundary Value Problem
In this paper, we establish some criteria for the existence of positive solutions for certain two point boundary value problems for the singular nonlinear second order equation −(ru ) + qu = λf (t, u ) on a time scale T. As a special case when T = R, our results include those of Erbe and Mathsen [11]. Our results are new in a general time scale setting and can be applied to difference and q-dif...
متن کاملOn a class of second-order impulsive boundary value problem at resonance
We consider the following impulsive boundary value problem, x′′(t) = f (t,x,x′), t ∈ J \ {t1, t2, . . . , tk}, x(ti)= Ii(x(ti),x′(ti)), x′(ti)= Ji(x(ti),x′(ti)), i= 1,2, . . . ,k, x(0)= 0, x′(1) = ∑m−2 j=1 αjx′(ηj). By using the coincidence degree theory, a general theorem concerning the problem is given. Moreover, we get a concrete existence result which can be applied more conveniently than r...
متن کاملA Third Order Nonlocal Boundary Value Problem at Resonance
We consider the third-order nonlocal boundary value problem u ′′′ (t) = f (t, u(t)), a.e. in (0, 1), u(0) = 0, u ′ (ρ) = 0, u ′′ (1) = λ[u ′′ ], where 0 < ρ < 1, the nonlinear term f satisfies Carathéodory conditions with respect to L 1 [0, T ], λ[v] = 1 0 v(t) dΛ(t), and the functional λ satisfies the resonance condition λ[1] = 1. The existence of a solution is established via Mawhin's coincid...
متن کاملSingular Second-order Multipoint Dynamic Boundary Value Problems with Mixed Derivatives
Singular nonlinear boundary value problems for differential equations and difference equations have been extensively studied in the literature; see [1, 4, 11, 12, 16, 18–22] and the references therein. However, the research for singular boundary value problems on time scales is still in its beginning stages. In [8], the authors investigate the existence of a positive solution for the three-poin...
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: International Journal of Differential Equations
سال: 2017
ISSN: 1687-9643,1687-9651
DOI: 10.1155/2017/8579065