On second order nonlocal boundary value problem at resonance
نویسندگان
چکیده
منابع مشابه
A 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 کاملOrder-type existence theorem for second order nonlocal problems at resonance
This paper gives an abstract order-type existence theorem for second order nonlocal boundary value problems at resonance and obtain existence criteria for at least two positive solutions, where $f$ is a continuous function. Our results generalize or extend related results in the literature and give a positive answer to the question raised in the literature. An example is given to illustr...
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 کاملBoundary Value Problem for Second-order Differential Operators with Mixed Nonlocal Boundary Conditions
In this paper, we study a second order differential operator with mixed nonlocal boundary conditions combined weighting integral boundary condition with another two point boundary condition. Under certain conditions on the weighting functions and on the coefficients in the boundary conditions, called non regular boundary conditions, we prove that the resolvent decreases with respect to the spec...
متن کاملNontrivial 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 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: Fasciculi Mathematici
سال: 2016
ISSN: 0044-4413
DOI: 10.1515/fascmath-2016-0010