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Realization theory methods for the stability investigation of nonlinear infinite-dimensional input-output systems

Volker Reitmann (2011)

Mathematica Bohemica

Realization theory for linear input-output operators and frequency-domain methods for the solvability of Riccati operator equations are used for the stability and instability investigation of a class of nonlinear Volterra integral equations in a Hilbert space. The key idea is to consider, similar to the Volterra equation, a time-invariant control system generated by an abstract ODE in a weighted Sobolev space, which has the same stability properties as the Volterra equation.

Reconstruction of map projection, its inverse and re-projection

Tomáš Bayer, Milada Kočandrlová (2018)

Applications of Mathematics

This paper focuses on the automatic recognition of map projection, its inverse and re-projection. Our analysis leads to the unconstrained optimization solved by the hybrid BFGS nonlinear least squares technique. The objective function is represented by the squared sum of the residuals. For the map re-projection the partial differential equations of the inverse transformation are derived. They can be applied to any map projection. Illustrative examples of the stereographic and globular Nicolosi projections...

Resonance and multiplicity in periodic boundary value problems with singularity

Irena Rachůnková, Milan Tvrdý, Ivo Vrkoč (2003)

Mathematica Bohemica

The paper deals with the boundary value problem u ' ' + k u = g ( u ) + e ( t ) , u ( 0 ) = u ( 2 π ) , u ' ( 0 ) = u ' ( 2 π ) , where k ∈ ℝ , g I ↦ ℝ is continuous, e ∈ 𝕃 J and lim x → 0 + ∫ x 1 g ( s ) d s = ∞ . In particular, the existence and multiplicity results are obtained by using the method of lower and upper functions which are constructed as solutions of related auxiliary linear problems.

Results on Non-resonant Oscillations for some Nonlinear Vector Fourth Order Differential Systems

Awar Simon Ukpera, Olufemi Adeyinka Adesina (2012)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

This paper presents vector versions of some existence results recently published for certain fourth order differential systems based on generalisations drawn from possibilities arising from the underlying auxiliary equation. The results obtained also extend some known works involving third order differential systems to the corresponding fourth order.

Retracts, fixed point index and differential equations.

Rafael Ortega (2008)

RACSAM

Some problems in differential equations evolve towards Topology from an analytical origin. Two such problems will be discussed: the existence of solutions asymptotic to the equilibrium and the stability of closed orbits of Hamiltonian systems. The theory of retracts and the fixed point index have become useful tools in the study of these questions.

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