Oscillation of a quasilinear impulsive delay parabolic equation with two different boundary conditions

In this paper, we discuss the oscillation for a class of quasilinear impulsive delay parabolic equations with two different boundary conditions and obtain several oscillation criteria.     

带有类p-Laplacian算子的Kirchhoff型方程的多重解

研究一类带有类p-Laplacian算子的Kirchhoff型方程.利用对称山路定理,得到了多重解存在的充分条件,推广和改进了已有结果.     

带有积分边界条件的一阶脉冲微分方程奇异边值问题

利用Schauder′s不动点定理研究带有积分边界条件的一阶脉冲微分方程奇异边值问题,得到正解的存在性结论.其中对应非脉冲情形的相关结论也是新的.     

二阶p-Laplace多参数离散周期边值问题三个解的存在性

研究了二阶p-Laplace含多个参数的非线性离散周期边值问题,获得了非线性项在更一般的情形下三个解的存在性定理.主要结论的证明基于临界点理论.     

LOWER BOUNDS ESTIMATE FOR THE BLOW-UP TIME OF A NONLINEAR NONLOCAL POROUS MEDIUM EQUATION＊

The lower bounds for the blow-up time of blow-up solutions to the nonlinear nolocal porous equation ut=Δum+up∫Ωuqdx with either null Dirichlet boundary condition or homogeneous Neumann boundary conditi...     

Mountain Pass solutions for quasi-linear equations via a monotonicity trick

We obtain the existence of symmetric Mountain Pass solutions for quasi-linear equations without the typical assumptions which guarantee the boundedness of an arbitrary Palais-Smale sequence. This is done through a recent version of the monotonicity trick proved in Squassina (in press) [22]. The main results are new also for the p-Laplacian operator.     

高阶椭圆算子Dirichlet本征值的下界

设Ω是R^m(m≥2）中的一个有界区域,其边界足够光滑,考察2p(p≥1）阶椭圆算子（－1）^p ∑│α│＝│β│＝pa^α(Aαβa^β)在Dirichlet边界条件下的本征值问题,给出了其本征值的一个下界,该下界除与维数m有关外仅依赖于区域Ω的体积。     

Nonlinearity and nontrivial solutions of fourth order semilinear elliptic equations

We consider the existence of nontrivial solutions of a fourth order semilinear elliptic boundary value problem with Dirichlet boundary condition, Δ²u+cΔu=b₁[(u+1)⁺−1]+b₂u⁺ in Ω, where Ω is a bounded open set in R^N with smooth boundary ∂Ω. The variation of linking theorem is useful to investigate them. We investigate them in six regions of (b₁,b₂) when λ₁<c<λ₂.     

TWO-POINT BOUNDARY VALUE PROBLEM FOR A CLASS OF SECOND-ORDER DIFFERENCE EQUATIONS

In this paper, we apply a critical point theorem and obtain the condition for the existence of three solutions to two-point boundary value problem of a second order nonlinear difference equation.     

A probabilistic approach to positive harmonic functions in a slab with alternating Dirichlet and Neumann boundary conditions

Let , , be a dimensional slab. Denote points by , where and . Denoting the boundary of the slab by , let

where is an ordered sequence of intervals on the right half line (that is, b_{n}$">). Assume that the lengths of the intervals are bounded and that the spaces between consecutive intervals are bounded and bounded away from zero. Let . Let and denote respectively the cone of bounded, positive harmonic functions in and the cone of positive harmonic functions in which satisfy the Dirichlet boundary condition on and the Neumann boundary condition on .

Letting , the main result of this paper, under a modest assumption on the sequence , may be summarized as follows when :

1. If , then and are both one-dimensional (as in the case of the Neumann boundary condition on the entire boundary). In particular, this occurs if with 2$">.

2. If and , then and is one-dimensional. In particular, this occurs if .

3. If , then and the set of minimal elements generating is isomorphic to (as in the case of the Dirichlet boundary condition on the entire boundary). In particular, this occurs if with .

When , as soon as there is at least one interval of Dirichlet boundary condition. The dichotomy for is as above.

     

The investigation of free vibrations for an asymmetric beam equation using category theory

We investigate free vibrations for an asymmetric beam equation. We find them by applying linking inequalities and the limit relative category theory.     

On the Existence of Positive Solutions of Quasilinear Elliptic Equations with Mixed Boundary Conditions

In this paper, the existence of positive solutions for the mixed boundary problem of quasilinear elliptic equation {-div (|∇u|^{p-2}∇u) = |u|^{p^∗-2}u + f(x, u), \quad u > 0, \quad x ∈ Ω u|_Γ_0 = 0, \frac{∂u}{∂\overrightarrow{n}}|_Γ_1 = 0 is obtained, where Ω is a bounded smooth domain in R^N, ∂Ω = \overrightarrow{Γ}_0 ∪ \overrightarrow{Γ}_1, 2 ≤ p < N, p^∗ = \frac{Np}{N-p}, Γ_0 and Γ_1 are disjoint open subsets of ∂Ω.     

两点边值条件热弹性收缩模型的线性稳定性

1Introduction Theanalysisofthermalcontactproblemshasrevealeawealthofinteresting phenomena.BeginningwithJ.R.Barberin1978[1],whopointedoutthatthesolutionof suchproblemsposescertaindifficulties,andcontinuingtothisday,numerousresearchers haveturnedtheirattent…