Expansion of a bundle of fourth-order differential operators in a part of its eigenfunctions

A bundle of differential operators

Existence of a family of soliton-like solutions for the Kawahara equation

Existence is proved for a family of soliton-like solutions for the nonlinear evolution equation u_t–+uu_x+u_xxx-u_xxxxx=O. The problem is reduced to investigating the fixed points of the operator

On the Center of the Generalized Liénard System

In this paper, we discuss the conditions for a center for the generalized Liénard system (E)₁

Markov-Bernstein-type inequalities for classes of polynomials with restricted zeros

We prove that an absolute constantc>0 exists such that

On the Dirichlet Problem in a Characteristic Rectangle for Fourth Order Linear Singular Hyperbolic Equations

In the rectangle D = (0,

Generalized System for Relaxed Cocoercive Variational Inequalities and Projection Methods

Let K be a nonempty closed convex subset of a real Hilbert space H. The approximate solvability of a system of nonlinear variational inequality problems, based on the convergence of projection methods, is discussed as follows: find an element (x*, y*)K×K such that

On solutions of elliptic differential equations with operator coefficients

It is proved that on a simply connected region the solutions of the elliptic partial differential equation have representations U(x,y) = QV(x,y), where V admits local power series expansion in the "operator variable" xI + yI and (Q,T) forms a standard pair for the monic operator polynomial A₀ + A₁ + + ^s-1A_s-1 + ^sI.This paper was written while the autor was employed at the Vrije Universiteit in Amsterdam.     

An oscillation criterion for functional differential equations with deviating arguments

An oscillation criterion is given for the differential equation

On the oscillation and asymptotic behavior of the solutions of a certain system of differential-functional equations of neutral type

Conditions for the oscillation of all solutions and for the existence of nonoscillatory solutions with polynomial growth at infinity are given for the system of differential-functional equations of neutral type

Generalized sine equations,II

In this paper we solve the equations

On the quasiarithmetic mean in a mean value property and the associated functional equation

The functional equation

Global Behavior of Rational Sequences Involving Piecewise Power Function

In this paper, we are concerned with the global behavior ofthe solutions of the difference equation

On nonoscillation of canonical or noncanonical disconjugate functional equations

Qualitative comparison of the nonoscillatory behavior of the equations

Jacobi elliptic functions and change of variable in a convolution

We solve the functional equation

Existence and uniqueness of limit cycles on a cubic kolmogorov differential system in the Predator-Prey relation

In this paper, we analyse qualitatively a cubic Kolmogorov system: which is one of the mathematical models in ecology describing the interaction between Predator-Prey of two populations; and give the conditions of nonexistence, existence and uniqueness of limit cycles for three different cases.Fulfilled during engagement in advanced studies at the Institute of Mathematics, Academia Sinica.     

On a class of nonlinear Schrödinger equations

This paper concerns the existence of standing wave solutions of nonlinear Schrödinger equations. Making a standing wave ansatz reduces the problem to that of studying the semilinear elliptic equation:

The Cauchy Problem for a Higher Order Telegraph Equation

Using the integral operator that defines a solution of the Cauchy problem for the equation

Existence of Solutions for the Dirichlet Problem with Superlinear Nonlinearities

In this paper we establish the existence of nontrivial solutions to

A quadrature rule for finite-part integrals

A quadrature rule is described for evaluating finite-part (f.p.) integrals of the form , witha 1. The rule is obtained by interpolating tof by a polynomial which coincides withf at the shifted zeros of a Legendre polynomial.     

Initial value problem for a class of nonlinear pseudo-hyperbolic equations

The existence of global weak solutions to the periodic boundary problem or the initial value problem for the nonlinear Pseudo-hyperbolic equation u_(tt)-[a_1+a_2(u_x)~(2m)]u_(xx)-a_3u_(xxt)=f(x,t,u,u_x) is proved by the method of the vanishing of the additional diffusion terms, Leray-Schauder's fixedpoint argument and Sobolev's estimates,where m≥1 is a natural number and a_i>0(i=1,2,3)are constants.