Existence of positive, negative and sign-changing periodic solutions for a class of integral equations

AbstractIn this paper, the simultaneous existence of positive, negative and sign-changing periodic solutions for a class of integral equations of the form ϕ(x)=∫[x,x+ω]∩ΩK(x,y)f(y,ϕ(y−τ(y)))dy,x∈Ω, is considered, where Ω is a closed subset of RN with a periodic structure. Our main result is different from most existing results since they provide three constant sign periodic solutions only

On a discrete nonlinear boundary value problem

AbstractThe nonlinear eigenvalue problem Δ2uk−1+λ|uk|γ=0,k=1,2,…,n under the Dirichlet boundary conditions u0=0=un+1 is studied. An existence and uniqueness theorem is proved. Qualitative properties of solutions are also given

Green's function and stability of a linear partial difference scheme

AbstractThis paper is concerned with a linear partial difference equation which arises from discretizing a heat and a first order wave equations. A Green's function for this equation is derived. Various representation theorems, monotonicity, and oscillatory properties of the Green's functions are obtained. Then by means of the representation theorems, we derive several stability criteria for arbitrary solutions of this equation

Kamenev type oscillation criteria for nonlinear difference equations

summary:By means of Riccati transformation techniques, we establish some new oscillation criteria for second-order nonlinear difference equation which are sharp

Existence and Uniqueness of Periodic Solutions for a Second-Order Nonlinear Differential Equation with Piecewise Constant Argument

Based on a continuation theorem of Mawhin, a unique periodic solution is found for a second-order nonlinear differential equation with piecewise constant argument

On a class of fourth order linear recurrence equations

This paper is concerned with sequences that satisfy a class of fourth order linear recurrence equations. Basic properties of such sequences are derived. In addition, we discuss the oscillatory and nonoscillatory behavior of such sequences

Monotone methods for a discrete boundary problem

AbstractThis paper is motivated by recent interests in space discrete Nagumo equations and is concerned with the existence of solutions of a nonlinear discrete boundary value problem. Monotone methods are used to derive the existence theorems. These methods, as is well known, provide constructive schemes for calculating the solutions

Regular starlike domains of tridiagonal matrices

AbstractThis paper is concerned with 2n-by-2n tridiagonal matrices with variable diagonal vectors. Sharp conditions (in terms of these vectors) for such matrices to be nonsingular are derived and stated in geometrical terms. Our results are motivated by observations on a simple two-by-two matrix