A state-space method for computing upper bounds for the peak of the structured singular value over frequency for both real and complex uncertainties is presented. These bounds are based on the positivity and Popov criteria for one-sided, sector-bounded and for norm-bounded, block-structured linear uncertainty. These criteria are restated and used to derive upper bounds for the peak structured s...

In this paper we prove the existence and uniqueness of strong solutions for the stochastic Navier-Stokes equation in bounded and unbounded domains. These solutions are stochastic analogs of the classical Lions-Prodi solutions to the deterministic Navier-Stokes equation. Local monotonicity of the nonlinearity is exploited to obtain the solutions in a given probability space and this significantl...

In this paper, a nonlinear elliptic boundary value problem with singular nonlinearity is studied, where L is a uniformly elliptic operator, is a bounded domain in R N , N 2, 0 may take the value 0 on @, and f(x; s) is possibly singular near s = 0. Some results regarding the existence of positive solutions for the problem are given under a set of hypotheses that make neither monotonicity nor str...

We consider the semilinear parabolic equation ut = ∆u+ up on RN , where the power nonlinearity is subcritical. We first address the question of existence of entire solutions, that is, solutions defined for all x ∈ RN and t ∈ R. Our main result asserts that there are no positive radially symmetric bounded entire solutions. Then we consider radial solutions of the Cauchy problem. We show that if ...

Uniqueness and continuous dependence of solutions of (2) can thus be derived from the well-posedness of the Cauchy problem for (3). We remark that the genuine nonlinearity of (1) implies that the total variation of u(t0, ·) is locally bounded, for each t0 > 0. Hence the well posedness of the Cauchy problem (3) with initial data x(t0) = x0 follows from [2]. It is worth noting that in [3] the wel...

In this article we consider the problem −∆pu − b (x) |∇u| p−1 = a (x) f (u) , u > 0 on R (N ≥ 3), lim|x|→∞ u(x) = 0. We prove that the considered problem has a bounded positive entire radial solution under some conditions on a, b and f . The method of proving theorems is essentially based on the shooting method. Our result, about the existence of radially symmetric solutions, seem to be the fir...

In this paper, a nonlinear elliptic boundary value problem with singular nonlinearity Lu(x) = f(x, u(x)), x ∈ Ω, u(x) = φ(x), x ∈ ∂Ω, is studied, where L is a uniformly elliptic operator, Ω is a bounded domain in R , N ≥ 2, φ ≥ 0 may take the value 0 on ∂Ω, and f(x, s) is possibly singular near s = 0. Some results regarding the existence of positive solutions for the problem are given under a s...

We study the nonlinearity of Exponential Welch Costas functions using the Fourier transform on Zn. Exponential Welch Costas functions are bijections from Zp−1 to Zp−1 defined using the exponential function of Zp, where p is an odd prime. Their linearity properties were recently studied by Drakakis, Requena, and McGuire, who conjectured that the absolute values of the Fourier coefficients of an ...

Dynamical properties of discrete solitons in nonlinear Schrödinger lattices with saturable nonlinearity are studied in the framework of the one-dimensional discrete Vinetskii-Kukhtarev model. Two stationary strongly localized modes, centered on site (A) and between two neighboring sites (B), are obtained. The associated Peierls-Nabarro potential is bounded and has multiple zeros indicating stro...

u(x, 0) = u0(x) and ut(x, 0) = u1(x) for x ∈ Ω, and u(x, t)|∂Ω = 0, t ≥ 0, (1.2) where Ω is a bounded domain in R with smooth, say C-class, boundary ∂Ω and σ(|∇u|) is a function like σ = 1/ √ 1 + |∇u|2, mean curvature type nonlinearity. The viscosity term −∆ut is often called a Kelvin-Voigt type dissipation or strong dissipation which appears in phenomena of wave propagation in a viscoelastic m...