Related papers: Continuation theorems for periodic systems and app…

We consider a diffusion $(\xi_t)_{t\ge 0}$ with some $T$-periodic time dependent input term contained in the drift: under an unknown parameter $\vth\in\Theta$, some discontinuity - an additional periodic signal - occurs at times…

In this paper we consider a class of nonlinear periodic differential systems perturbed by two nonlinear periodic terms with multiplicative different powers of a small parameter $e>0$. For such a class of systems we provide conditions which…

We give a sufficient condition for the surjectivity of partial differential operators with constant coefficients on a class of distributions on R^{n+1} (here we think of there being n space directions and one time direction), that are…

We study ordinary differential equations of the type $u^{(n)}(t)=f(u(t))$ with initial conditions $u(0) = u'(0) =... = u^{(m-1)}(0) = 0 $ and $u^{(m)}(0) \neq 0$ where $m \geq n$, no additional assumption is made on $f$. We establish some…

In this paper, we prove existence results of a one-dimensional periodic solution to equations with the fractional Laplacian of order $s\in(1/2,1)$, singular nonlinearity, and gradient term under various situations, including nonlocal…

This paper deals with various cases of resonance, which is a fundamental concept of science and engineering. Specifically, we study the connections between periodic and unbounded solutions for several classes of equations and systems. In…

In this paper we study the existence and continuation of solution to general fractional differential equation with Hilfer fractional derivative. First we establish new local existence theorems. Then we derive the continuation theorems. With…

In this paper we give an extension of the Birkhoff--Lewis theorem to some semilinear PDEs. Accordingly we prove existence of infinitely many periodic orbits with large period accumulating at the origin. Such periodic orbits bifurcate from…

We consider a linear differential system of Mathieu equations with periodic coefficients over periodic closed orbits and we prove that, arbitrarily close to this system, there is a linear differential system of Hamiltonian damped Mathieu…

We consider the non-degenerate second-order parabolic partial differential equations of non-divergence form with bounded measurable coefficients (not necessary continuous). Under some assumptions it is known that the fundamental solution to…

In this paper we evaluate the topological index of periodic solutions otained via the Malkin-Loud bifurcation result. Incidentally, we do not assume that the perturbation is differentiale.

This paper provides a dynamical frame to study non-autonomous parabolic partial differential equations with finite delay. Assuming monotonicity of the linearized semiflow, conditions for the existence of a continuous separation of type II…

We present an illustrative application of the two famous mathematical theorems in differential topology in order to show the existence of periodic orbits with arbitrary given period for a class of hamiltonians .This result point out for a…

We obtain sufficient conditions ensuring the existence of a uniformly continuous and H\"older continuous homeomorphism between the solutions of a linear system of differential equations with piecewise constant argument of generalized type…

We introduce a new approach for the study of the Problem of Iterates using the theory on general ultradifferentiable structures developed in the last years. Our framework generalizes many of the previous settings including the Gevrey case…

The existence and multiplicity of positive periodic solutions for first non-autonomous singular systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter. The proof of our…

In the present paper we derive Liouville type results and existence of periodic solutions for $\chi^{(2)}$ type systems with non-homogeneous nonlinearities. Moreover, we prove both universal bounds as well as singularity and decay estimates…

We prove that the seasonally-forced SIR model with a T-periodic forcing has a periodic solution with period T whenever the basic reproductive number R0>1. The proof uses the Leray-Schauder degree theory. We also describe some numerical…

We develop a Galois theory for systems of linear difference equations with periodic parameters, for which we also introduce linear difference algebraic groups. We then apply this to constructively test if solutions of linear q-difference…

In this paper we prove unique continuation principles for some systems of elliptic partial differential equations satisfying a suitable superlinearity condition. As an application, we obtain nonexistence of nontrivial (not necessarily…