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

     

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:

     

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

The nonlinear nth-order singular nonlocal boundary value problem

     

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 ,

     

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

     

Degenerate bifurcation points of periodic solutions of autonomous Hamiltonian systems

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

     

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

     

A restricted sum formula among multiple zeta values

For positive integers α₁,α₂,…,αr with αr?2, the multiple zeta value or r-fold Euler sum is defined as

     

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

The equation

     

Layered solutions for a semilinear elliptic system in a ball

We consider the following system of Schrödinger-Poisson equations in the unit ball B₁ of R³:

     

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