Related papers: Iterative oscillation tests for differential equat…
The linear boundary value problem under consideration describes time-harmonic motion of water in a horizontal three-dimensional layer of constant depth in the presence of an obstacle adjacent to the upper side of the layer (floating body).…
In this work, Lienard equations are considered. The limit cycles of these systems are studied by applying the homotopy analysis method. The amplitude and frequency obtained with this methodology are in good agreement with those calculated…
We present a methodology for numerically integrating ordinary differential equations containing rapidly oscillatory terms. This challenge is distinct from that for differential equations which have rapidly oscillatory solutions: here the…
We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…
In this paper we study the existence of radially symmetric solitary waves in R^N for the nonlinear Klein-Gordon equations coupled with the Maxwell's equations when the nonlinearity exhibits critical growth. The main feature of this kind of…
This paper presents a modified iterative approach to solve the variational inequality problem using the double inertial technique in the context of a real Hilbert space. Our iterative technique involves a projection onto a generalized…
The long time effect of nonlinear perturbation to oscillatory linear systems can be characterized by the averaging method, and we consider first-order averaging for its simplest applicability to high-dimensional problems. Instead of the…
We introduce a discrete-time fractional calculus of variations. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. They…
We obtain local (i.e., linearized) convergence conditions for iterative methods that seek solitary waves with prescribed values of quadratic conserved quantities of multi-component Hamiltonian nonlinear wave equations. These conditions…
Time-decaying harmonic oscillators yield dispersive estimates with weak decay, and change the threshold power of the nonlinearity between the short and the long range. In the non-critical case for the time-decaying harmonic oscillator, this…
We present an analytical study of a nonlinear oscillator subject to an additive Ornstein-Uhlenbeck noise. Known results are mainly perturbative and are restricted to the large dissipation limit (obtained by neglecting the inertial term) or…
We prove the existence and uniqueness of the solution to the doubly nonlinear parabolic systems with mixed boundary conditions. Due to the unilateral constraint the problem comes as a variational inequality. We apply the penalty method and…
We establish two nonlinear retarded integral inequalities. Bounds on the solution of some retarded equations are then obtained.
This article provides a general iterative approximation to partial differential equations, and thus establish existence of smooth solution. The heart of the method is to contract (or expand) the boundary conditions uniformly in the domain,…
The rich non-linear dynamics of the coupled oscillators (under second harmonic injection) can be leveraged to solve computationally hard problems in combinatorial optimization such as finding the ground state of the Ising Hamiltonian. While…
In this article we study optimal control problems for systems that are affine with respect to some of the control variables and nonlinear in relation to the others. We consider finitely many equality and inequality constraints on the…
We provide of a method to integrate first order non-linear systems of differential equations with variable coefficients. It determines approximate solutions given initial or boundary conditions or even for Sturm-Liouville problems. This…
We study a family of Li\'enard--type equations. Such equations are used for the description of various processes in physics, mechanics and biology and also appear as traveling--wave reductions of some nonlinear partial differential…
Some properties of global solution of scalar Riccati equation are studied. On the basis of these properties using the Whiburn's and Leighton - Nehary's theorems some oscillatory and criteria are proved for second order linear systems of…
We consider the oscillatory integrals with parameter-dependent phases. We decompose the integrals into a leading term and a remainder term. Instead of the pointwise estimate, we use some $L^p$-estimate for the remainder term and get various…