The oscillation of a differential equation of second order with deviating argument
The oscillation of linear first order differential systems.
The oscillatory behavior of second order nonlinear elliptic equations.
The -Laplacian and connected pairs of functions.
The parabolic equations as a limiting case of hyperbolic and elliptic equations
The period function near a polycycle with two semi-hyperbolic vertices
The period of a whirling pendulum
The period function of a planar parameter-depending Hamiltonian system is examined. It is proved that, depending on the value of the parameter, it is either monotone or has exactly one critical point.
The period of oscillations in non-linear systems
The periodic Ambrosetti-Prodi problem for nonlinear perturbations of the p-Laplacian
We prove an Ambrosetti–Prodi type result for the periodic solutions of the equation , when is arbitrary and or when . The proof uses upper and lower solutions and the Leray–Schauder degree.
The periodic boundary value problem for some second order ordinary differential equations
The periodic problem for semilinear differential inclusions in Banach spaces
Sufficient conditions on the existence of periodic solutions for semilinear differential inclusions are given in general Banach space. In our approach we apply the technique of the translation operator along trajectories. Due to recent results it is possible to show that this operator is a so-called decomposable map and thus admissible for certain fixed point index theories for set-valued maps. Compactness conditions are formulated in terms of the Hausdorff measure of noncompactness.
The periodic problem for the second order integro-differential equations with distributed deviation
We study the question of the unique solvability of the periodic type problem for the second order linear integro-differential equation with distributed argument deviation and on the basis of the obtained results by the a priori boundedness principle we prove the new results on the solvability of periodic type problem for the second order nonlinear functional differential equations, which are close to the linear integro-differential equations. The proved results are optimal in some sense.
The periodic solutions of the compound singular fractional differential system with delay.
The periods of the Volterra-Lotka system.
The permanence in a single species nonautonomous system with delays and feedback control.
The Perron product integral and generalized linear differential equations
The pertubatively stable spectrum of a periodic Schrödinger operator.
The pharmacodynamics of antibiotic treatment.
The Poincaré-Bendixson Theorem: from Poincaré to the XXIst century
The Poincaré-Bendixson Theorem and the development of the theory are presented - from the papers of Poincaré and Bendixson to modern results.
The principle of stationary action in the calculus of variations
We review some techniques from non-linear analysis in order to investigate critical paths for the action functional in the calculus of variations applied to physics. Our main intention in this regard is to expose precise mathematical conditions for critical paths to be minimum solutions in a variety of situations of interest in Physics. Our claim is that, with a few elementary techniques, a systematic analysis (including the domain for which critical points are genuine minima) of non-trivial models...