Exponential stability of nonautonomous linear differential equations with linear perturbations by Liao methods

In this paper, the author considers, by Liao methods, the stability of Lyapunov exponents of a nonautonomous linear differential equations: with linear small perturbations. It is proved that, if A(t) is a upper-triangular real n by n matrix-valued function on R₊, continuous and uniformly bounded, and if there is a relatively dense sequence in R₊, say 0=T₀<T₁<?<Ti<?, such that

     

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

     

The topology of the monodromy map of a second order ODE

We consider the following question: given A∈SL(2,R), which potentials q for the second order Sturm-Liouville problem have A as its Floquet multiplier? More precisely, define the monodromy map μ taking a potential q∈L²([0,2π]) to , the lift to the universal cover of SL(2,R) of the fundamental matrix map ,

     

The stability of the equilibrium of the damped oscillator with damping changing sign

In this paper, we prove a sufficient and necessary condition for the stability of the equilibrium x=x^′=0 of the damped oscillator with damping changing sign

     

Positive solutions for nonlinear nth-order singular eigenvalue problem with nonlocal conditions

The nonlinear nth-order singular nonlocal boundary value problem

     

Existence of multiple positive solutions of singular nonlinear boundary value problems

For a given positive integer N, we provide conditions on the nonlinear function f which guarantee that the boundary value problem

     

Multiple positive solutions for a quasilinear elliptic equation with critical exponential nonlinearity

Let Ω be a bounded domain in R^N,N≥2, with C² boundary. In this work, we study the existence of multiple positive solutions of the following problem:

     

Second order singular boundary value problems with integral boundary conditions

We study the second order singular boundary value problem

     

Heteroclinic connections for fully non-linear non-autonomous second-order differential equations

We investigate the solvability of the following strongly non-linear non-autonomous boundary value problem

     

Stability properties of solutions of linear second order differential equations with random coefficients

The equation

     

Degenerate bifurcation points of periodic solutions of autonomous Hamiltonian systems

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