Regularity for a fourth-order critical equation with gradient nonlinearity

Given Ω a smooth bounded domain of Rn, n?3, we consider functions that are weak solutions to the equation

     

Stability of an alternative functional equation

Let map an abelian semigroup (S,+) into a Banach space (X‖⋅‖). We deal with stability of the following alternative functional equation

     

The solution manifold and C-smoothness for differential equations with state-dependent delay

Let h>0, open, and continuously differentiable. If f satisfies two mild additional smoothness conditions then the set

     

The chain rule as a functional equation

We consider operators T from C¹(R) to C(R) satisfying the “chain rule”

     

Periodic solutions of Duffing equations with semi-quadratic potential and singularity

In this paper, we deal with the existence of periodic solutions of the second order differential equations x^″+g(x)=p(t) with singularity. We prove that the given equation has at least one periodic solution when g(x) has singularity at origin, satisfies

     

Iterative equations in Banach spaces

Let X be a Banach space, let

     

Stability problem of Ulam for generalized forms of Cauchy functional equation

Let G₁ be a vector space and G₂ a Banach space. In this paper, we solve the generalized Hyers-Ulam-Rassias stability problem for a generalized form

     

Regularity of solutions on the global attractor for a semilinear damped wave equation

We consider attractors Aη, η∈[0,1], corresponding to a singularly perturbed damped wave equation

     

Stability for the time-dependent Hartree equation with positive energy

In this paper, we show that the H¹ solutions to the time-dependent Hartree equation

     

On the Laplace equation with dynamical boundary conditions of reactive-diffusive type

This paper deals with the Laplace equation in a bounded regular domain Ω of RN (N?2) coupled with a dynamical boundary condition of reactive-diffusive type. In particular we study the problem

     

Unique continuation property for a higher order nonlinear Schrödinger equation

We prove that, if a sufficiently smooth solution u to the initial value problem associated with the equation

     

Solvability of the resonant 1-dimensional periodic p-Laplacian equations

In this paper we study the existence of 2π-periodic solutions of

     

Solutions to critical elliptic equations with multi-singular inverse square potentials

Let Ω be an open-bounded domain in R^N(N?3) with smooth boundary ∂Ω. We are concerned with the multi-singular critical elliptic problem

     

On solvability of boundary value problems for higher order nonlinear hyperbolic equations

In the rectangle Ω=[0,a]×[0,b] for the nonlinear hyperbolic equation

the boundary value problems of the type

are considered, where and are linear bounded functionals.Sufficient conditions of solvability and unique solvability of the general problem and its particular cases (Nicoletti type, Dirichlet, Lidstone and Periodic problems) are established.     

On a max-type and a min-type difference equation

This note shows that every positive solution to the following third order non–autonomous max-type difference equation

when is a three-periodic sequence of positive numbers, is periodic with period three. The same result was proved for the following min-type difference equation

     

Generalized quadratic mappings of r-type in several variables

Let X,Y be vector spaces. It is shown that if an even mapping satisfies f(0)=0, and

(∗)     

Schröder equation and commuting functions on the circle

We show that if is a homeomorphism of the unit circle S¹ and the rotation number α(F) of F is irrational, then the Schröder equation

     

On existence and asymptotic stability of solutions of the degenerate wave equation with nonlinear boundary conditions

We study the global existence of solutions of the nonlinear degenerate wave equation (ρ?0)