Stability of periodic solutions of state-dependent delay-differential equations

We consider a class of autonomous delay-differential equations

     

Multiplicity results for periodic solutions to delay differential equations via critical point theory

By the critical point theory, we study the existence and multiplicity of periodic solutions to the following system of delay differential equations:

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Superstability and rigorous asymptotics in singularly perturbed state-dependent delay-differential equations

We study the singularly perturbed state-dependent delay-differential equation

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On existence of periodic solutions of Rayleigh equation of retarded type

Existence of periodic solutions for a kind of non-autonomous Rayleigh equations of retarded type

x^″(t)+f(t,x^′(t-σ))+g(t,x(t-τ(t)))=p(t)$x^{″}(t)+f(t,x^{\prime }(t-\sigma ))+g(t,x(t-\tau (t)))=p(t)$

On the distribution of zeros of solutions of first order delay differential equations

This paper contains new estimates for the distance between adjacent zeros of solutions of the first order delay differential equation

x^′(t)+p(t)x(t−τ)=0     

Degenerate bifurcation points of periodic solutions of autonomous Hamiltonian systems

We study connected branches of nonconstant 2π-periodic solutions of the Hamilton equation

     

Nonoscillation and positivity of solutions to first order state-dependent differential equations with impulses in variable moments

The state-dependent delay differential equation

     

Almost periodic and almost automorphic solutions of linear differential/difference equations without Favard's separation condition. I

The well-known Favard's theorem states that the linear differential equation

(1)     

Exact asymptotic behavior near the boundary to the solution for singular nonlinear Dirichlet problems

We take up the existence and the exact asymptotic behavior near the boundary ∂Ω of the unique classical solution to a singular Dirichlet problem

     

A class of nonlinear evolution equations subjected to nonlocal initial conditions

We prove the existence of C⁰-solutions for a class of nonlinear evolution equations subjected to nonlocal initial conditions, of the form:

     

New results of periodic solutions for forced Rayleigh-type equations

In this paper, we use the coincidence degree theory to establish new results on the existence and uniqueness of T$T$-periodic solutions for a kind of forced Rayleigh equation of the form

x^″+f(t,x^′(t))+g(t,x(t))=e(t).$x^{″}+f(t,x^{\prime }\left(t\right))+g(t,x\left(t\right))=e\left(t\right)\text{.}$

On periodic solutions of second-order differential equations with attractive-repulsive singularities

Sufficient conditions for the existence of a solution to the problem

     

Inverse spectral problems for Bessel operators

We study the inverse spectral problem for a class of Bessel operators given in L₂(0,1) by the differential expression

     

Almost periodic and almost automorphic solutions of linear differential/difference equations without Favard's separation condition. II

In this paper we continue the research started in a previous paper, where we proved that the linear differential equation

(1)