Periodic solutions of nonlinear functional difference equations at nonresonance case

Sufficient conditions for the existence of at least one T-periodic solution of nonlinear functional difference equation

Δx(n)+a(n)x(n)=f(n,u(n)),     

Oscillation for nonlinear second order dynamic equations on a time scale

We obtain some oscillation criteria for solutions to the nonlinear dynamic equation

xΔΔ+q(t)xΔσ+p(t)(f○xσ)=0,     

Oscillation criteria for second-order nonlinear delay dynamic equations

In this paper, we consider the second-order nonlinear delay dynamic equation

(r(t)xΔ(t)Δ⁾+p(t)f(x(τ(t)))=0,     

A nonhomogeneous elliptic problem involving critical growth in dimension two

In this paper we study a class of nonhomogeneous Schrödinger equations

−Δu+V(x)u=f(u)+h(x)     

Compactly supported solutions to stationary degenerate diffusion equations

We consider non-negative solutions of the semilinear elliptic equation in Rn with n?3:

−Δu=a(x)uq+b(x)up,     

Existence of solutions for a cantilever beam problem

We are concerned with the fourth-order nonuniform cantilever beam problem

(I(x)WΔ∇(x)⁾Δ∇=f(x,W(x)),     

A functional equation having monomials as solutions

For each n=1,2,3, we obtain the general solution and the stability of the functional equation

f(2x+y)+f(2x-y)=2^n-2[f(x+y)+f(x-y)+6f(x)].     

Radial ground states and singular ground states for a spatial-dependent p-Laplace equation

We consider the following equation

Δpu(x)+f(u,|x|)=0,     

Solution of Hyers-Ulam stability problem for generalized Pappus' equation

The purpose of this paper is to solve the stability problem of Ulam for an approximate mapping of the following generalized Pappus' equation:

n²Q(x+my)+mnQ(x−ny)=(m+n)[nQ(x)+mQ(ny)]     

The stability of Cauchy's gamma-beta functional equation

We obtain the super stability of Cauchy's gamma-beta functional equation

B(x,y)f(x+y)=f(x)f(y),     

Oscillation criteria for half-linear dynamic equations on time scales

This paper is concerned with oscillation of the second-order half-linear dynamic equation

(r(t)(xΔγ⁾Δ⁾+p(t)xγ(t)=0,     

Absence of point spectrum for unitary operators

Let us consider the time-dependent Schrödinger equation,

iφt=−Δφ+V(x,t)φ,     

Kamenev-type oscillation criteria for second order nonlinear dynamic equations on time scales

The purpose of this paper to establish oscillation criteria for second order nonlinear dynamic equation

(r(t)(x^Δ(t))^γ)^Δ+f(t,x(g(t)))=0,     

Linearized oscillation of odd order nonlinear neutral delay differential equations (I)

In this paper, we proved that the odd order nonlinear neutral delay differential equation

[x(t)−p(t)g(x(t−τ))^](n)+q(t)h(x(t−σ))=0     

On a direct method for proving the Hyers-Ulam stability of functional equations

We study the stability of an equation in a single variable of the form

f(x)=af(h(x))+bf(−h(x))     

Stability problem for the Go?a?b-Schinzel type functional equations

Let X be a vector space over a field K of real or complex numbers, n∈N and λ∈K?{0}. We study the stability problem for the Go?a?b-Schinzel type functional equations

f(x+fn(x)y)=λf(x)f(y)     

A mean value theorem for cubic fields

Let r(n) denote the number of integral ideals of norm n in a cubic extension K of the rationals, and define and Δ(x)=S(x)−αx where α is the residue of the Dedekind zeta function ζ(s,K) at 1. It is shown that the abscissa of convergence of

     

On solutions of a common generalization of the Go?a?b-Schinzel equation and of the addition formulae

Under some additional assumptions we determine solutions of the equation

f(x+M(f(x))y)=f(x)○f(y),     

On the two-dimensional stationary Schrödinger equation with a singular potential

We study the equation

−△u(x,y)+ν(x,y)u(x,y)=0     

Oscillation and nonoscillation criteria for second order quasilinear difference equations

New oscillation and nonoscillation theorems are obtained for the second order quasilinear difference equation

Δ(|Δxn−1|^ρ−1Δxn−1)+pn|xn|^ρ−1xn=0,