Related papers: Iterative oscillation tests for difference equatio…
An ordinary differential equation perturbed by a null-recurrent diffusion will be considered in the case where the averaging type perturbation is strong only when a fast motion is close to the origin. The normal deviations of these…
We study the rate of convergence for (variational) eigenvalues of several non-linear problems involving oscillating weights and subject to different kinds of boundary conditions in bounded domains.
In this paper, we present a method to identify integrable complex nonlinear oscillator systems and construct their solutions. For this purpose, we introduce two types of nonlocal transformations which relate specific classes of nonlinear…
New criteria are established for upper bounds on the number of limit cycles of periodic Abel differential equations having two periodic invariant curves, one of them bounded. The criteria are applied to obtain upper bounds of either zero or…
Argumentation is a non-monotonic process. This reflects the fact that argumentation involves uncertain information, and so new information can cause a change in the conclusions drawn. However, the base logic does not need to be…
We provide a new result on the existence of extremal solutions for second-order Dirichlet problems with deviation argument. As a novelty in this work, the nonlinearity need not be continuous or monotone. In order to obtain this new result,…
We consider a stable but nearly unstable autoregressive process of any order. The bridge between stability and instability is expressed by a time-varying companion matrix $A_{n}$ with spectral radius $\rho(A_{n}) < 1$ satisfying…
A general nonautonomous Nicholson equation with multiple pairs of delays in {\it mixed monotone} nonlinear terms is studied. Sufficient conditions for permanence are given, with explicit lower and upper uniform bounds for all positive…
We prove the existence of nonlinear normal modes for general systems of two coupled nonlinear oscillators. Facilitating the comparison principle for ordinary differential equations it is shown that there exist exact solutions representing a…
This paper extends the discriminant associated to second order linear constant coefficient differential equations to general second order linear differential equations. The main result of this paper is that the discriminant of a second…
In this paper we consider a class of fourth order nonlinear integro-differential equations with Navier boundary conditions. By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and…
We explore a nonlocal connection between certain linear and nonlinear ordinary differential equations (ODEs), representing physically important oscillator systems, and identify a class of integrable nonlinear ODEs of any order. We also…
The aim of this paper is to employ variational techniques and critical point theory to prove some conditions for the existence of solutions to nonlinear impulsive dynamic equation with homogeneous Dirichlet boundary conditions. Also we will…
Considerable interest has recently been focused on studying multiple phenotypes simultaneously in both epidemiological and genomic studies, either to capture the multidimensionality of complex disorders or to understand shared etiology of…
We consider nonlinear elliptic systems satisfying componentwise coercivity condition. The nonlinear terms have controlled growths with respect to the solution and its gradient, while the behaviour in the independent variable is governed by…
We use the entropy method to analyze the nonlinear dynamics and stability of a continuum kinetic model of an active nematic suspension. From the time evolution of the relative entropy -- an energy-like quantity in the kinetic model -- we…
Short nonstandard proofs are given for some results about infinite systems of equations in infinitely many variables.
In this work we establish existence and multiplicity of solutions for elliptic problem with nonlinear boundary conditions under strong resonance conditions at infinity. The nonlinearity is resonance at infinity and the reso- nance phenomena…
Under a Morse index condition we prove symmetry results for solutions of a nonlinear mixed boundary condition elliptic problem. As an intermediate step we relate the Morse index of a solution to a mixed boundary condition linear eigenvalue…
In this paper, we analyze nonlinear differential equations subject to generalized boundary conditions. More specifically, we provide a framework from which we can provide conditions, which are straightforward to check, for the solvability…