A class of strongly cooperative systems without compactness
A Classification Of Solutions Of Second Order Linear Differential Equations By Means Of Regularly Varying Functions
A direct proof of a theorem by Kolmogorov in hamiltonian systems
A limit set trichotomy for order-preserving systems on time scales.
A new instability result to nonlinear vector differential equations of fifth order.
A new theorem on exponential stability of periodic evolution families on Banach spaces.
A note on the exponential stability of a matrix Riccati equation of stochastic control
A principle of linearization in theory of stability of solutions of variational inequalities
It is shown that the uniform exponential stability and the uniform stability at permanently acting disturbances of a sufficiently smooth but not necessarily steady-state solution of a general variational inequality is a consequence of the uniform exponential stability of a zero solution of another (so called linearized) variational inequality.
A proof of the two-dimensional Markus-Yamabe Stability Conjecture and a generalization
The following problem of Markus and Yamabe is answered affirmatively: Let f be a local diffeomorphism of the euclidean plane whose jacobian matrix has negative trace everywhere. If f(0) = 0, is it true that 0 is a global attractor of the ODE dx/dt = f(x)? An old result of Olech states that this is equivalent to the question if such an f is injective. Here the problem is treated in the latter form by means of an investigation of the behaviour of f near infinity.
A remark on the half-linear extension of the Hartman-Wintner theorem.
A Remark on the Oscillatoriness of Solutions of a Non-Linear Third-Order Equation
A spectral mapping theorem for semigroups solving PDEs with nonautonomous past.
A stability theory for perturbed differential equations.
A three-species food chain system with two types of functional responses.
A two-dimensional model for the transmission of dengue fever disease.
A useful proposition to nonlinear differential systems with a solution of the prescribed asymptotic properties
A weak invariance principle and asymptotic stability for evolution equations with bounded generators.
About uniform boundedness and convergence of solutions of certain nonlinear differential equations of fifth-order.
Additive groups connected with asymptotic stability of some differential equations
The asymptotic behaviour of a Sturm-Liouville differential equation with coefficient is investigated, where and is a nondecreasing step function tending to as . Let denote the set of those ’s for which the corresponding differential equation has a solution not tending to 0. It is proved that is an additive group. Four examples are given with , , (i.e. the set of dyadic numbers), and .
Almost Floquet and generalized almost Floquet systems