Let a,b (b > a) be nonnegative integers. We define the discrete interval [a,b] = {a,a + 1, . . . ,b}. All other intervals will carry its standard meaning, for example, [0,∞) denotes the set of nonnegative real numbers. The symbol Δ denotes the forward difference operator with step size 1, that is, Δu(k) = u(k + 1)− u(k). Furthermore for a positive m, Δm is defined as Δmu(k)= Δm−1(Δu(k)). In thi...

In this paper, we study the existence of positive solutions for a system fractional differential equations with ?-Laplacian operators, Riemann–Liouville derivatives diverse orders and general nonlinearities which depend on several integrals differing orders, supplemented nonlocal coupled boundary conditions containing Riemann–Stieltjes varied derivatives. The from are continuous nonnegative fun...

An important part is played in the theory of control by special matrix equations [i], and also by the matrix inequalities associated with them. The solutions of these equations or inequalities allow us to construct Lyapunov functions for nonlinear systems of automatic regulation, and to solve problems of the synthesis of optimal control with quadratic quality criterion. Convenient and effective...

Hysteresis in material behaviour includes both signum nonlinearities as well as high dimensionality. Available models for component-level hysteretic behaviour are empirical. Here, we derive a low-order model for rate-independent hysteresis from a high-dimensional massless frictional system. The original system, being given in terms of signs of velocities, is first solved incrementally using a l...

This paper presents a procedure for the identification of two types of a continuous-time linear system interconnected by direct and feedback memoryless nonlinearities. The first case is the continuous time Hammesrstein system and the second is a specific case of the continuous time Wiener system. The direct and feedback nonlinear elements, described by bounded unknown functions, are expressed a...

In this paper we generalize previous work on the spectral and orbital stability of waves for infinite-dimensional Hamiltonian systems to include those cases for which the skewsymmetric operator J is singular. We assume that J restricted to the orthogonal complement of its kernel has a bounded inverse. With this assumption and some further genericity conditions we (a) derive an unstable eigenval...

We prove the existence of radial solutions of the quasilinear elliptic equation div(A(|Du|)Du) + f(u) = 0 in R, n > 1, where f is either negative or positive for small u > 0, possibly singular at u = 0, and growths subcritically for large u. Our proofs use only elementary arguments based on a variational identity. No differentiability assumptions are made on f .

We consider a stochastic partial differential equation with two logarithmic nonlinearities, with two reflections at 1 and −1 and with a constraint of conservation of the space average. The equation, driven by the derivative in space of a space-time white noise, contains a bi-Laplacian in the drift. The lack of the maximum principle for the bi-Laplacian generates difficulties for the classical p...

Recommended by Pavel Drabek We study existence and multiplicity of positive solutions for the following Dirichlet equations: −Δu − μ/|x| 2 u λfx|u| q−2 u gx|u| 2 * −2 u in Ω, u 0 on ∂Ω, where 0 ∈ Ω ⊂ R N N ≥ 3 is a bounded domain with smooth boundary ∂Ω, λ > 0, 0 ≤ μ < μ N − 2 2 /4, 2 * 2N/N − 2, 1 ≤ q < 2, and f, g are continuous functions on Ω which are somewhere positive but which may change...

‎this paper presents two main results that the singular values of the hadamard product of normal matrices $a_i$ are weakly log-majorized by the singular values of the hadamard product of $|a_{i}|$ and the singular values of the sum of normal matrices $a_i$ are weakly log-majorized by the singular values of the sum of $|a_{i}|$‎. ‎some applications to these inequalities are also given‎. ‎in addi...