Boundary Value Problems - Latest Articles

Nonsimple material problems addressed by the Lagrange's identity

Marin Marin — 2013-05-20T00:00:00Z

Our paper is concerned with some basic theorems for nonsimple thermoelastic materials. By using the Lagrange identity, we prove the uniqueness theorem and some continuous dependence theorems without recourse to any energy conservation law, or to any boundedness assumptions on the thermoelastic coefficients. Moreover, we avoid the use of positive definiteness assumptions on the thermoelastic coefficients.

The local strong and weak solutions to a generalized Novikov equation

Shaoyong Lai — 2013-05-20T00:00:00Z

A nonlinear partial differentialequation, which includes the Novikov equation as a special case, is investigated.The well-posedness oflocal strong solutions for the equation in the Sobolev space $H^s(R)$ with$s>\frac{3}{2}$ is established. Although the $H^1$-norm of the solutions to the nonlinear model doesnot remain constants, the existence of its local weak solutions in the lowerorder Sobolev space $H^s(R)$ with $1\leq s\leq\frac{3}{2}$ is establishedunder the assumptions $u_0\in H^s$ and $\parallelu_{0x}\parallel_{L^\infty}<\infty$.

Stability analysis for impulsive stochastic fuzzy p-Laplace dynamic equations under Neumann or Dirichlet boundary condition

Ruofeng Rao — 2013-05-20T00:00:00Z

Under Neumann or Dirichlet boundary condition, the stability of a class of delayed impulsive Markovian jumping stochastic fuzzy p-Laplace partial differential equations (PDEs) is considered. Thanks to some methods differentfrom those of previous literature, the difficulties brought byfuzzy stochastic mathematical model and impulsive model were overcome. By way of the Lyapunov-Krasovskiifunctional, Ito formula, Dynkin formula and a differentialinequality, new LMI-based global stochastic exponential stability criteria for the above-mentioned PDEs are established. Some applications of the obtained results improve some existing results on neural networks. And some numerical examples are presented to illustrate the effectiveness of the proposed method due to thesignificant improvement in the allowable upper bounds of time delays.

Approximation of Eigenvalues of Discontinuous Sturm-Liouville Problems with eigenparameter in all Boundary Conditions

Mohamed Tharwat — 2013-05-20T00:00:00Z

In this paper, we apply a sinc-Gaussian technique to computeapproximate values of the eigenvalues of Sturm-Liouville problems which contain an eigenparameter appearing linearly in two boundary conditions, in addition to an internal point of discontinuity. The error of this method decays exponentially in terms of the number of involved samples. Therefore the accuracy of the new technique is higher than the classical sinc method. Numerical worked examples with tables and illustrative figures are given at the end of the paper.

Mathematical aspects of Heisenberg uncertainty principle within local fractional Fourier analysis

Xiao-Jun Yang — 2013-05-20T00:00:00Z

In this paper, we discuss the mathematical aspects of Heisenberg uncertainty principle within local fractional Fourier analysis. The Schrodinger equation and Heisenberg uncertainty principles are structured within local fractional operators.

Existence of a solution for a three-point boundary value for a second-order differential equation at resonance

Juan Nieto — 2013-05-20T00:00:00Z

We present a new existence result for a second order nonlinear ordinary differential equation with three-point boundary value problem when the linear part is noninvertible.

Periodic Solutions for N+2-Body Problems with N+1 Fixed Centers

Fengying Li — 2013-05-17T00:00:00Z

In this paper, we prove the existence of a new periodic solution for N+2-body problems with N+1 fixed centers and strong-force potentials, in this model, N particles with equal masses are fixed at the vertices of a regular N-gon and the (N+1)-th particle is fixed at the center of the N-gon, the (N+2)-th particle winding around N particles.

Uniform attractors for the non-autonomous $p$-Laplacian equations with dynamic flux boundary conditions

Kun Li — 2013-05-17T00:00:00Z

This paper studies the long time asymptotic behavior of solutions for the non-autonomous $p$- Laplacian equations with dynamicflux boundary conditions in $n$-dimensional bounded smooth domains.We have proved the existence of the uniform attractor in $L^2(\bar{\Omega},d\mu)$ for the non-autonomous p-Laplacianevolution equations subject to dynamic nonlinear boundary conditions by using the Sobolev embedding theory, and the existence of the uniformattractor in $\left(W^{1,p}(\Omega)\cap L^q(\Omega)\right)\times L^q(\Gamma)$ by asymptotic a priori estimate.

Existence of nonnegative solutions for a fractional m-point boundary value problem at resonance

Qu HaiDong — 2013-05-16T00:00:00Z

In this paper, we consider the existence of nonnegative solutions for fractional m-point boundary value problem. The parameters in the multi-point boundary conditions are such that the corresponding differential operator is non-invertible but nevertheless is a Fredholm map of index zero. As a result the minimal and maximal nonnegative solution for the problem are obtained by using a fixed point theorem of increasing operators.

Particular Solutions of a Certain Class of Associated Cauchy-Euler Fractional Partial Differential Equation via Fractional Calculus

Shy-Der Lin — 2013-05-16T00:00:00Z

In recent years, various operators of fractional calculus (that is, calculus of integrals and derivatives of arbitrary real or complex orders) have been investigated and applied in many remarkably diverse fields of science and engineering. Many authors have demonstrated the usefulness of fractional calculus in the derivation of particular solutions of a number of linear ordinary and partial differential equations of the second and higher orders. The purpose of this paper is to present a certain class ofthe explicit particular solutions of associated Cauchy-Euler fractional partial differential equation of arbitrary real or complex orders and their applications.