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This paper is concerned with the existence and uniqueness of random periodic solutions for stochastic differential equations (SDEs), where the drift terms involved need not to be uniformly dissipative. On the one hand, via the reflection…
In this paper, we study the existence of bifurcation of a van der Pol-Duffing oscillator with quintic terms and its quasi-periodic solutions by means of qualitative and bifurcation theories. Firstly, we analyze the autonomous system and…
Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics and engineering to medicine and economics. These systems cannot be properly modelled and simulated with standard…
In this paper we investigate the impact of delayed tax revenues on the fiscal policy out-comes. Choosing the delay as a bifurcation parameter we study the direction and the stability of the bifurcating periodic solutions. With respect to…
In this work we study the existence of periodic and asymptotically periodic solutions of a system of nonlinear Volterra difference equations with infinite delay. By means of fixed point theory, we furnish conditions that guarantee the…
We study networks of theta neurons arranged on a ring with delayed interactions. In the continuum limit the systems are described by next generation neural field models with delays. We consider distributed delays with both finite and…
Bifurcations of periodic orbits as an external parameter is varied are a characteristic feature of generic Hamiltonian systems. Meyer's classification of normal forms provides a powerful tool to understand the structure of phase space…
This paper deals with the boundary value problems for the singularly perturbed differential-algebraic system of equations. The case of turning points has been studied. The sufficient conditions for existence and uniqueness of the solution…
Partial differential equations with discrete (concentrated) state-dependent delays in the space of continuous functions are investigated. In general, the corresponding initial value problem is not well posed, so we find an additional…
We prove a sharp version of the Hopf boundary point lemma for Black-Scholes type equations. We also investigate the existence and the regularity of the spatial derivative of the solutions at the spatial boundary.
This paper is devoted to study the existence of solutions and the monotone method of second-order periodic boundary value problems when the lower and upper solutions $\alpha$ and $\beta$ violate the boundary conditions $…
Existence and spatio-temporal patterns of periodic solutions to second order reversible equivariant autonomous systems with commensurate delays are studied using the Brouwer $O(2) \times \Gamma \times \mathbb Z_2$-equivariant degree theory,…
We consider methods based on the topological degree theory to compute periodic orbits of area preserving maps. Numerical approximations of the Kronecker integral and the application of Stenger's method allows us to compute the value of the…
The existence and spatio-temporal patterns of $2\pi$-periodic solutions to second order reversible equivariant autonomous systems with commensurate delays are studied using the Brouwer $O(2) \times \Gamma \times \mathbb Z_2$-equivariant…
In this paper, we approximate the solution and also discuss the periodic behavior termed as eventual periodicity of solutions of (IBVPs) for some dispersive wave equations on a bounded domain corresponding to periodic forcing. The…
In this paper we solve the eigenvalue problem of stochastic Hamiltonian system with boundary conditions. Firstly, we extend the results in S. Peng \cite{peng} from time-invariant case to time-dependent case, proving the existence of a…
In this paper we rigorously prove the existance of a non-trivial periodic orbit for the non-linear delay differential equation: $x'(t) = K \sin(x(t-1))$ for $K=1.6$. We show that the equations on the Fourier equations have a solution by…
We show how a variant of the Lefschetz Fixed Point Theorem may be used to count the number of periodic orbits for certain rational difference equations.
This paper focuses on the delay induced Hopf bifurcation in a dual model of Internet congestion control algorithms which can be modeled as a time-delay system described by a one-order delay differential equation (DDE). By choosing…
In this paper, we used some theorems of fixed point for studying the results of Existence and Uniqueness For Hilfer-Hadamard-Type Fractional Differential Equations, \[_{H}D^{\alpha,\beta}x(t)+f(t,x(t))=0, ~~~~~~ on~~the~~ interval~~…