Superlinear singular problems on the half line.
Symmetry in a certain simply perturbed Hamiltonian system
The boundary curves of three classes of the second order nonlinear ordinary differential equations
The distance between fixed points of some pairs of maps in Banach spaces and applications to differential systems
Let be a -contraction on a Banach space and let be an almost -contraction, i.e. sum of an -contraction with a continuous, bounded function which is less than in norm. According to the contraction principle, there is a unique element in for which If moreover there exists in with , then we will give estimates for Finally, we establish some inequalities related to the Cauchy problem.
The fixed point theorem and the boundedness of solutions of differential equations in the Banach space
The properties of solutions of the nonlinear differential equation in a Banach space and of the special case of the homogeneous linear differential equation are studied. Theorems and conditions guaranteeing boundedness of the solution of the nonlinear equation are given on the assumption that the solutions of the linear homogeneous equation have certain properties.
The General Differential Operators Generated by a Quasi-Differential Expressions with their Interior Singular Points
The general ordinary quasi-differential expression M of n-th order with complex coefficients and its formal adjoint M + are considered over a regoin (a, b) on the real line, −∞ ≤ a < b ≤ ∞, on which the operator may have a finite number of singular points. By considering M over various subintervals on which singularities occur only at the ends, restrictions of the maximal operator generated by M in L2|w (a, b) which are regularly solvable with respect to the minimal operators T0 (M ) and T0...
The initial boundary value problem of a mixed-typed hemivariational inequality.
The method of lower and upper solutions for some fourth-order equations.
The role of an integral inequality in the study of certain differential equations.
The set of first-order differential equations with periodic or bounded solutions.
The objective of this note is the announcement of two results of Ambrosetti-Prodi type concerning the existence of periodic (respectively bounded) solutions of the first order differential equation x' = f (t,x).
Topogical equivalence of monotone nonlinear nonautonomous differential equations
Totally bounded differential polynomial systems in
Totally bounded differential systems in are defined as having all trajectories bounded. By Dulac’s finiteness theorem it is proved that totally bounded polynomial systems exhibit an unbounded «annulus» of cycles. The portrait of the remaining trajectories is examined in the case the system has, in , a unique singular point. Work is in progress concerning the study of totally bounded polynomial systems with two singular points.
Trichotomy and bounded solutions of nonlinear differential equations
The existence of bounded solutions for equations in Banach spaces is proved. We assume that the linear part is trichotomic and the perturbation satisfies some conditions expressed in terms of measures of noncompactness.
Über das Anwachsen der Lösungen homogener algebraischer Differentialgleichungen zweiter Ordnung.
Über die Beschränktheit und die Existenz von Lösungen der Differentialgleichung 4. Ordnung mit nacheilendem Argument
Über die Existenz einer begrenzten und periodischen Lösung der nichtlinealisierten Jacobischen Gleichung mit negativ definitivem Träger
Über die Trichotomie von Lösungen einer nichtlinearen Vektordifferentialgleichung zweiter Ordnung
Über eine nichtlineare parametrische Differentialgleichung dritter Ordnung
Über eine Verallgemeinerung der Nicoletti-Aufgabe für Funktional-Differentialgleichungen mit voreilendem Argument.
Ultimate boundedness of some third order ordinary differential equations
We prove the ultimate boundedness of solutions of some third order nonlinear ordinary differential equations using the Lyapunov method. The results obtained generalize earlier results of Ezeilo, Tejumola, Reissig, Tunç and others. The Lyapunov function used does not involve the use of signum functions as used by others.