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### Exact controllability of a non-linear generalized damped wave equation: Application to the sine-Gordon equation.

Electronic Journal of Differential Equations (EJDE) [electronic only]

### Center manifold and exponentially-bounded solutions of a forced Newtonian system with dissipation.

Electronic Journal of Differential Equations (EJDE) [electronic only]

### Interior controllability of a $2×2$ reaction-diffusion system with cross-diffusion matrix.

Boundary Value Problems [electronic only]

### Interior controllability of a broad class of reaction diffusion equations.

Mathematical Problems in Engineering

### Controllability of second-order equations in ${L}^{2}\left(\text{Ω}\right)$.

Mathematical Problems in Engineering

### Variation of constants formula for functional parabolic partial differential equations.

Electronic Journal of Differential Equations (EJDE) [electronic only]

### On the controllability of a type of large scale CNN with delays.

Divulgaciones Matemáticas

### Controllability of the Strongly Damped Wave Equation with Impulses and Delay

Nonautonomous Dynamical Systems

Evading fixed point theorems we prove the interior approximate controllability of the following semilinear strongly damped wave equation with impulses and delay [...] in the space Z1/2 = D((−Δ)1/2)×L2(Ω),where r > 0 is the delay, Γ = (0, τ)×Ω, ∂Γ = (0, τ) × ∂Ω, Γr = [−r, 0] × Ω, (ϕ,ψ) ∈ C([−r, 0]; Z1/2), k = 1, 2, . . . , p, Ω is a bounded domain in ℝℕ(ℕ ≥ 1), ω is an open nonempty subset of , 1 ω denotes the characteristic function of the set ω, the distributed control u ∈ L2(0, τ; U), with...

### Controllability of the Semilinear Heat Equation with Impulses and Delay on the State

Nonautonomous Dynamical Systems

In this paper we prove the interior approximate controllability of the following Semilinear Heat Equation with Impulses and Delay [...] where Ω is a bounded domain in RN(N ≥ 1), φ : [−r, 0] × Ω → ℝ is a continuous function, ! is an open nonempty subset of Ω, 1ω denotes the characteristic function of the set ! and the distributed control u be- longs to L2([0, τ]; L2(Ω; )). Here r ≥ 0 is the delay and the nonlinear functions f , Ik : [0, τ] × ℝ × ℝ → ℝ are smooth enough, such that [...] Under this...

### A Representation Theorem for $\varphi$-Bounded Variation of Functions in the Sense of Riesz

Commentationes Mathematicae

In this paper we extend the well known Riesz lemma to the class of bounded $\varphi$-variation functions in the sense of Riesz defined on a rectangle ${I}_{a}^{b}\subset {ℝ}^{2}$. This concept was introduced in [2], where the authors proved that the space $B{V}_{\varphi }^{R}\left({I}_{a}^{b};ℝ$ of such functions is a Banach Algebra. Moreover, they characterized also the Nemytskii operator acting in this space. Thus our result creates a continuation of the paper [2].

### On the Hammerstein equation in the space of functions of bounded $\varphi$-variation in the plane

Archivum Mathematicum

In this paper we study existence and uniqueness of solutions for the Hammerstein equation $u\left(x\right)=v\left(x\right)+\lambda {\int }_{{I}_{a}^{b}}K\left(x,y\right)f\left(y,u\left(y\right)\right)\phantom{\rule{0.166667em}{0ex}}dy\phantom{\rule{0.166667em}{0ex}},\phantom{\rule{1.0em}{0ex}}x\in {I}_{a}^{b}:=\left[{a}_{1},{b}_{1}\right]×\left[{a}_{2},{b}_{2}\right]\phantom{\rule{0.166667em}{0ex}},$ in the space $B{V}_{\varphi }^{ℝ}\left({I}_{a}^{b}\right)$ of function of bounded total $\varphi -$variation in the sense of Riesz, where $\lambda \in ℝ$, $K:{I}_{a}^{b}×{I}_{a}^{b}\to ℝ$ and $f:{I}_{a}^{b}×ℝ\to ℝ$ are suitable functions.

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