By using the fixed-point index theorem, we consider the existence of positive solutions for the following nonlinear higher-order four-point singular boundary value problem on time scales uΔ n t g t f u t , uΔ t , . . . , uΔ n−2 t 0, 0 < t < T ; uΔ i 0 0, 0 ≤ i ≤ n−3; αuΔ 0 −βuΔ ξ 0, n ≥ 3; γuΔ T δuΔ η 0, n ≥ 3, where α > 0, β ≥ 0, γ > 0, δ ≥ 0, ξ, η ∈ 0, T , ξ < η, and g : 0, T → 0, ∞ is rd-con...

Elmendorf’s Theorem in equivariant homotopy theory states that for any topological group G, the model category of G-spaces is Quillen equivalent to the category of continuous diagrams of spaces indexed by the opposite of the orbit category of G with the projective model structure. For discrete G, Bert Guillou explored equivariant homotopy theory for any cofibrantly generated model category C an...

We prove common fixed point theorems for two pairs of hybrid mappings satisfying implicit relations in complete metric spaces using the concept of R−weak commutativity of type AT and we correct errors of [1], [3] and [8]. Our theorems generalize results of [1-3], [8], [12-16] and [21].

In this paper, we discuss the existence, nonexistence, and multiplicity of positive solutions for a class of singular eigenvalue problems. Some of our theorems are new, while others extend earlier results obtained by Zhang and Kong [12]. The interesting point is that the authors obtain the relation between the existence of solutions and the parameter λ. The arguments are based on the fixed poin...

This paper is concerned with the multiplicity of positive solutions of boundary value problem for the fourth-order quasilinear singular differential equation (|u|u) = λg(t)f(u), 0 < t < 1, where p > 1, λ > 0. We apply the fixed point index theory and the upper and lower solutions method to investigate the multiplicity of positive solutions. We have found a threshold λ < +∞, such that if 0 < λ ≤...

We define a family of differential operators indexed with fixed point free partitions. When these differential operators act on normalized power sum symmetric functions qλ(x), the coefficients in the decomposition of this action in the basis qλ(x) are precisely those of the decomposition of products of corresponding conjugacy classes of the symmetric group Sn . The existence of such operators p...

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 study m-point boundary value problem for fourth-order ordinary differential equation with bending term x00 8 0096-3 doi:10. * Co E-m xð4ÞðtÞ 1⁄4 gðtÞf ðt; xðtÞ; x00ðtÞÞ; t 2 ð0; 1Þ; xð0Þ 1⁄4 0; xð1Þ 1⁄4 P m 2 i1⁄41 aixðniÞ; x00ð0Þ 1⁄4 0; x00ð1Þ 1⁄4 P m 2 i1⁄41 bixðniÞ; <>: where 0 1⁄4 n0 < n1 < n2 < < nm 2 < nm 1 1⁄4 1. By constructing an available integral operator and combin...