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  • Boundedness of solution  (1)
  • Lebesgue-Stieltjes cost functionals  (1)
  • Ritz-Trefftz method  (1)
  • a priori error bounds
  • 1
    Electronic Resource
    Electronic Resource
    Global behaviour of age-dependent logistic population models (1990)
    Springer
    Journal of mathematical biology 28 (1990), S. 225-235 
    Details
    ISSN: 1432-1416
    Keywords: Logistic growth ; Age-dependent model ; Global stability ; Oscillation ; Boundedness of solution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We study the large time behaviour of a nonlinear population model with a general logistic term. It is proved that every solution must have a limit when time becomes infinite. We present conditions that guarantee the boundedness of the solution. Furthermore, we prove that in general no oscillation is possible for the total number of population. This is in sharp contrast to the linear case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00163146
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Minimum principle for systems with boundary conditions and cost having Stieltjes-type integrals (1981)
    Springer
    Journal of optimization theory and applications 33 (1981), S. 557-573 
    Details
    ISSN: 1573-2878
    Keywords: Minimum principle ; Stieltjes boundary constraints ; Lebesgue-Stieltjes cost functionals ; infinite-time problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Pontryagin's minimum principle for nonlinear differential systems with Stieltjes boundary constraints and performance index with an integral of the Lebesgue-Stieltjes type is derived. The case of infinite time is also considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935758
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Variational approximations in energy space for the regulator problem with time delay (1980)
    Springer
    Journal of optimization theory and applications 30 (1980), S. 293-307 
    Details
    ISSN: 1573-2878
    Keywords: Spline approximation ; energy space ; time-delay systems ; Ritz-Trefftz method ; a priori error bounds ; a posteriori error bounds
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider a variational procedure for approximating the solution of the state regulator problem with time delay. Motivated by a dual formulation of the problem, we introduce a positive-definite functionalF over a certain energy space of Mikhlin and obtain approximating solutions by the Ritz-Trefftz idea of minimizing it over finite-dimensional subspaces. The resulting approximating solutions, in turn, furnish suboptimal solutions which converge to the optimal solution of the regulator problem with time delay. A priori error bounds in terms of splines are given. A posteriori error bounds are also obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934500
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    Paper (German National Licenses)
    Fulltext
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