First integrals for the Duffing-Van der Pol type oscillator.
First integrals for two linearly coupled nonlinear Duffing oscillators.
First order elliptic systems and the existence of homoclinic orbits in Hamiltonian systems.
First order impulsive differential inclusions with periodic conditions.
First order integro-differential equations in Banach algebras involving Carathéodory and discontinuous nonlinearities.
First order linear ordinary differential equations in associative algebras.
First phases of the associated equation with parameters for the differential equation
First-order autoregressive processes with time-dependent random parameters
First-order differential equations of the hyperbolic type.
First-order differential equations with several deviating arguments: Sturmian comparison method in oscillation theroy: I.
First-order singular and discontinuous differential equations.
Five integral inequalities; an inheritance from Hardy and Littlewood.
Five limit cycles for a simple cubic system.
We resolve the centre-focus problem for a specific class of cubic systems and determine the number of limit cycles which can bifurcate from a fine focus. We also describe the methods which we have developed to investigate these questions in general. These involve extensive use of Computer Algebra; we have chosen to use REDUCE.
Fixed point analysis for non-oscillatory solutions of quasi linear ordinary differential equations
The paper deals with the quasi-linear ordinary differential equation with . We treat the case when is not necessarily monotone in its second argument and assume usual conditions on and . We find necessary and sufficient conditions for the existence of unbounded non-oscillatory solutions. By means of a fixed point technique we investigate their growth, proving the coexistence of solutions with different asymptotic behaviors. The results generalize previous ones due to Elbert–Kusano, [Acta...
Fixed point techniques and stability in nonlinear neutral differential equations with variable delays
Fixed point theorem in uniform spaces and applications
Fixed point theorems for multivalued mappings
Fixed points and controllability in delay systems.
Fixed points and differential equations with asymptotically constant or periodic solutions.
Fixed points and solutions of boundary value problems at resonance
We consider a simple boundary value problem at resonance for an ordinary differential equation. We employ a shift argument and construct a regular fixed point operator. In contrast to current applications of coincidence degree, standard fixed point theorems are applied to give sufficient conditions for the existence of solutions. We provide three applications of fixed point theory. They are delicate and an application of the contraction mapping principle is notably missing. We give a partial explanation...