In this paper, we investigate the existence of positive solutions for a class of singular nth-order three-point boundary value problem. The associated Green’s function for the boundary value problem is given at first, and some useful properties of the Green’s function are obtained. The main tool is fixed-point index theory. The results obtained in this paper essentially improve and generalize s...

By using the fixed-point index theory and Leggett-Williams fixed-point theorem,we study the existence of multiple solutions to the three-point boundary value problem u′′′ t a t f t, u t , u′ t 0, 0 < t < 1; u 0 u′ 0 0; u′ 1 − αu′ η λ, where η ∈ 0, 1/2 , α ∈ 1/2η, 1/η are constants, λ ∈ 0,∞ is a parameter, and a, f are given functions. New existence theorems are obtained, which extend and comple...

‎in this paper‎, ‎by using four functionals fixed point theorem‎, ‎we obtain sufficient conditions for the existence of‎ ‎at least one positive solution of an $n$th-order $m$-point boundary value problem‎. ‎as an application‎, ‎we give an example to demonstrate our main result.

In this work, we are concerned with the existence and the multiplicity of nontrivial positive solutions for a boundary value problem of a system of second-order differential equations subject to an integral boundary condition and posed on the positive half-line. The positive nonlinearities depend on the solution and their derivatives and may have space singularities. New existence results of si...

We prove new results on the existence of positive solutions for some cantilever equation subject to nonlocal and nonlinear boundary conditions. Our main ingredient is the classical fixed point index.

By some analysis of the neutral operator (Ax)(t) = x(t)− ∑n i=1 cix(t− δi) and an application of the fixed-point index theorem, we obtain sufficient conditions for the existence, multiplicity and nonexistence of periodic solutions to a second-order differential equation with the prescribed neutral operator, which improve and extend some recent results of Lu-Ge, WuWang, and Zhang. An example is ...

We discuss the existence of solutions for the first-order multipoint BVPs on time scale T: uΔ t p t u σ t λf t, u σ t , t ∈ 0, T T , u 0 − ∑mi 1 αiu ξi 0, where λ > 0 is a parameter, T > 0 is a fixed number, 0, T ∈ T, f : 0, T T × 0,∞ → 0,∞ is continuous, p is regressive and rdcontinuous, αi ≥ 0, ξi ∈ T, i 1, 2, . . . , m, 0 ξ0 < ξ1 < ξ2 < · · · < ξm−1 < ξm σ T , and 1 −∑mi 1 αi/ep ξi, 0 > 0. F...

In this paper, we investigate nonlinear fractional differential equations of arbitrary order with advanced arguments    D 0+u(t) + a(t)f(u(θ(t))) = 0, 0 < t < 1, n− 1 < α ≤ n, u(i)(0) = 0, i = 0, 1, 2, · · · , n− 2, [D 0+ u(t)]t=1 = 0, 1 ≤ β ≤ n− 2, where n > 3 (n ∈ N), D 0+ is the standard Riemann-Liouville fractional derivative of order α, f : [0,∞) → [0,∞), a : [0, 1] → (0,∞) and θ : (0, ...