Estimating the diameter of one class of functions in L2

Let

具时滞的奇异(n-1,1)共轭边值问题的多重正解

Abstract. This paper discusses the singular (n-l, 1) conjugate boundary value problem as fol-lows by using a fixed point index theorem in cones     

Existence of Positive Solutions for a Class of Sigular Boundary Value Problem of Fourth Order

Some results concerning existence of positive solutions for the singular boundary value problems u^(4)(t)=f(t,u(t)) t∈（0,1) u(0)=u(1)=0 u‘(0)=u‘(1)=0 have been given, where f(t, x) may be singular at t = 0, 1.     

Estimates for eigenvalues of Laplacian operator with any order

Let D be a bounded domain in an n-dimensional Euclidean space Rn. Assume that 0 ＜ λ1 ≤λ2 ≤ … ≤ λκ ≤ … are the eigenvalues of the Dirichlet Laplacian operator with any order l{(-△)lu=λu, in D u=(δ)u/(δ)(→n)=…(δ)l-1u/(δ)(→n)l-1=0,on (δ)D.Then we obtain an upper bound of the (k 1)-th eigenvalue λκ 1 in terms of the first k eigenvalues.k∑i=1(λκ 1-λi) ≤ 1/n[4l(n 2l-2)]1/2{k∑i=1(λκ 1-λi)1/2λil-1/l k∑i=1(λκ 1-λi)1/2λ1/li}1/2.This ineguality is independent of the domain D. Furthermore, for any l ≥ 3 the above inequality is better than all the known results. Our rusults are the natural generalization of inequalities corresponding to the case l = 2 considered by Qing-Ming Cheng and Hong-Cang Yang. When l = 1, our inequalities imply a weaker form of Yang inequalities. We aslo reprove an implication claimed by Cheng and Yang.     

Mixed boundary-value problems for singular second-order ordinary differential equations

It is proved that the boundary-value problem

Forward dynamical problem for the Timoshenko beam

The initial boundary value problem

Profile of Blow-up Solution to Hyperbolic System with Nonlocal Term

This paper is concerned with a nonlocal hyperbolic system as follows utt = △u ＋ （∫Ωvdx ）^p for x∈R^N,t〉0 ,utt = △u ＋ （∫Ωvdx ）^q for x∈R^N,t〉0 ,u（x,0）=u0（x）,ut（x,0）=u01（x） for x∈R^N,u（x,0）=u0（x）,ut（x,0）=u01（x） for x∈R^N, where 1≤ N ≤3, p ≥1, q ≥ 1 and pq 〉 1. Here the initial values are compactly supported and Ω belong to R^N is a bounded open region. The blow-up curve, blow-up rate and profile of the solution are discussed.     

On a Singular Two-Point Boundary Value Problem for the Nonlinear mth-Order Differential Equation with Deviating Arguments

Sufficient conditions of solvability and unique solvability of the boundary value problem are established, where are measurable functions and the vector function is measurable in the first and continuous in the last kmn arguments; moreover, this function may have nonintegrable singularities with respect to the first argument.     

Quasilinearization and Rate of Convergence for Higher-Order Nonlinear Periodic Boundary-Value Problems

We study the convergence of a sequence of approximate solutions for thefollowing higher-order nonlinear periodic boundary–value problem:

Oscillation of even order nonlinear functional differential equations with damping

This paper is concerned with a class of even order nonlinear damped differential equations

Solvability of a class of elastic beam equations with strong Carathéodory nonlinearity

We study the existence of a solution to the nonlinear fourth-order elastic beam equation with nonhomogeneous boundary conditions

Solvability of a higher-order multi-point boundary value problem at resonance

Based on the coincidence degree theory of Mawhin, we get a new general existence result for the following higher-order multi-point boundary value problem at resonance

On Existence and Multiplicity of Solutions for Elliptic Equations Involving the p-Laplacian

In the present paper, the following Dirichlet problem and Neumann problem involving the p-Laplacian

On the Order of Magnitude of the Divisor Function

Let D be an increasing sequence of positive integers, and consider the divisor functions： d（n, D） =∑d｜n,d∈D,d≤√n1, d2（n,D）=∑[d,δ]｜n,d,δ∈D,[d,δ]≤√n1, where [d,δ]=1.c.m.（d,δ）. A probabilistic argument is introduced to evaluate the series ∑n=1^∞and（n,D） and ∑n=1^∞and2（n,D）.     

Best polynomial approximation in Sobolev-Laguerre and Sobolev-Legendre spaces

We investigate limiting behavior as γ tends to ∞ of the best polynomial approximations in the Sobolev-Laguerre space W^N,2([0, ∞); e^−x) and the Sobolev-Legendre space W^N,2([−1, 1]) with respect to the Sobolev-Laguerre inner product

Strict inequalities for the derivatives of functions satisfying certain boundary conditions

For functions satisfying the boundary conditions

Multiple Existence of Nonradial Positive Solutions for a Coupled Nonlinear Schrödinger System

In this paper, we consider the multiple existence of nonradial positive solutions of coupled nonlinear Schr?dinger system

Existence of solutions for singular boundary problems for higher order differential equations

We offer sufficient conditions for the existence of solutions for the boundary value problem $\begin{gathered} y(n) + f(t,y,y^1 ,...,y^{(n - 2)} = 0, 0< t< 1, n \geqslant 2 \\ y^{(i)} (0) = 0, 0 \leqslant i \leqslant n - 3 \\ y^{(n - 2)} (0) - \beta y^{(n - 1)} (0) = 0 \\ \gamma y^{(n - 2)} (1) + \delta y^{(n - 1)} (1) = 0 \\ \end{gathered} $ where α, β, γ and δ are constants satisfying αγ+αδ+βγ>0, β, δ≥0, β+α>0 and δ+γ>0.     

具超前变元的二阶微分方程三点边值问题的正解

§ 1　 IntroductionRecently,certain three-point boundary value problems for nonlinear ordinarydifferential equations have been studied by many authors[1— 6] .However,few papers havebeen published on the same problems for nonlinear functional differential equations.In thispaper,we are concerned with the following second order differential equation with anadvanced argumentu″(t) +λa(t) f(u(h(t) ) ) =0 ,t∈ (0 ,1 ) (1 .1 )with the three-point boundary conditionsu(0 ) =0 ,αu(η) =u(1 ) ,(1 .2 )…