Solvability of boundary value problem for second order impulsive differential equations with one-dimensional p-Laplacian on whole line

This paper is concerned with a class of boundary value problems of the impulsive differential equations with one-dimensional p-Laplacian on whole line with a nonCarathéeodory nonlinearity. Sufficient conditions to guarantee the existence of solutions are established. Some examples are given to illustrate the main results

Existence of solutions of multi-term fractional differential equations with impulse effects on a half line

A class of boundary value problem for impulsive fractional differential equation on a half line is proposed. Some results on existence of solutions of this kind of boundary value problem for impulsive multi-term fractional differential equation on a half line are established by constructing a weighted Banach space, a completely continuous operator and using a fixed point theorem in the Banach space. Some unsuitable lemmas in recent published papers are pointed out. An example is given to illustrate the efficiency of the main theorems

Multiple Bounded Positive Solutions to Integral Type BVPs for Singular Second Order ODEs on the Whole Line

This paper is concerned with the integral type boundary value problems of the second order differential equations with one-dimensional p-Laplacian on the whole line. By constructing a suitable Banach space and a operator equation, sufficient conditions to guarantee the existence of at least three positive solutions of the BVPs are established. An example is presented to illustrate the main results. The emphasis is put on the one-dimensional p-Laplacian term [ρ(t)Φ(x’(t))]’ involved with the function ρ, which makes the solutions un-concave

Probing the twist-3 multi-gluon correlation functions by pp \to DX

We study the single spin asymmetry (SSA) for the D-meson production $A_N^D$ in the $pp$ collision, $p^\uparrow p\to DX$, in the framework of the collinear factorization. Since the charm quark is mainly produced through the $c\bar{c}$-pair creation from the gluon-fusion process, this is an ideal process to probe the twist-3 triple-gluon correlation functions in the polarized nucleon. We derive the corresponding cross section formula for the contribution of the triple-gluon correlation function to $A_N^D$ in $p^\uparrow p\to DX$, applying the method developed for $ep^\uparrow\to eDX$ in our previous study. As in the case of $ep^\uparrow\to eDX$, our result differs from a previous study in the literature. We will also present a simple estimate of the triple-gluon correlation functions based on the preliminary data on $A_N^D$ by RHIC.Comment: to appear in the proceedings of the 19th International Spin Physics Symposium (Spin2010), Sept.27 - Oct.2, 2010, Juelich, Germany, 5 pages, 2 figure

Triple positive solutions of BVP for second order ODE with one dimensional Laplacian on the half line

By applying Leggett-Williams fixed point theorem in a suitably constructed cone, we obtain the existence of at least three bounded positive solutions for a boundary value problem on the half line. Our result improves and complements some of the work in the literature

Positive solutions for (n−1,1) three-point boundary value problems with coefficient that changes sign

AbstractIn this paper, we establish existence results for positive solutions for the (n−1,1) three-point boundary value problems consisting of the equation u(n)+λa(t)fu(t)=0,t∈(0,1), with one of the following boundary value conditions: u(0)=αu(η),u(1)=βu(η),u(i)(0)=0fori=1,2,…,n−2, and u(n−2)(0)=αu(n−2)(η),u(n−2)(1)=βu(n−2)(η),u(i)(0)=0fori=0,1,…,n−3, where η∈(0,1), α⩾0, β⩾0, and a:(0,1)→R may change sign and R=(−∞,+∞). f(0)>0, λ>0 is a parameter. Our approach is based on the Leray–Schauder degree theory. This paper is motivated by Eloe and Henderson (Nonlinear Anal. 28 (1997) 1669–1680)

A Study of Impulsive Multiterm Fractional Differential Equations with Single and Multiple Base Points and Applications

We discuss the existence and uniqueness of solutions for initial value problems of nonlinear singular multiterm impulsive Caputo type fractional differential equations on the half line. Our study includes the cases for a single base point fractional differential equation as well as multiple base points fractional differential equation. The asymptotic behavior of solutions for the problems is also investigated. We demonstrate the utility of our work by applying the main results to fractional-order logistic models