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  • 1
    Electronic Resource
    Electronic Resource
    A mountain pass method for the numerical solution of semilinear wave equations (1993)
    Springer
    Numerische Mathematik 64 (1993), S. 487-509 
    Details
    ISSN: 0945-3245
    Keywords: 65M60
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary It is well-known that periodic solutions of semilinear wave equations can be obtained as critical points of related functionals. In the situation that we studied, there is usually an obvious solution obtained as a solution of linear problem. We formulate a dual variational problem in such a way that the obvious solution is a local minimum. We then find additional non-obvious solutions via a numerical mountain pass algorithm, based on the theorems of Ambrosetti, Rabinowitz and Ekeland. Numerical results are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01388701
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  • 2
    Electronic Resource
    Electronic Resource
    Finite difference approximations to the Dirichlet problem for elliptic systems (1986)
    Springer
    Numerische Mathematik 49 (1986), S. 227-237 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N05 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The Dirichlet problem foru=(u 1,...,u n ) $$\Delta u + f(x,u) = 0in\Omega ,u = 0on\Gamma = \partial \Omega $$ wheref=(f 1,...,f n ), is discretized in the usual way (h mesh size): $$\Delta ^h u + f(x,u) = 0in\Omega _h ,u = 0on\Gamma _h $$ We consider variousmonotone, convergent iterative schemes. Among others, they can be used, together with estimation theorems for upper and lower solutions, to show uniqueness for solutions of (2). Numerical results are given for the system $$\Delta u + u(a - bu - c\upsilon ) = 0,\Delta \upsilon + \upsilon (d - eu - f\upsilon ) = 0$$ from mathematical biology (two competing species). It is shown that there is a unique positive solution for certain values of the positive parametersa,..., f. This result is crucial for the asymptotic behavior of solutions of the corresponding parabolic system ast→∞.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389626
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Laparoscopic removal of translocated intrauterine contraceptive devices (1982)
    Oxford, UK : Blackwell Publishing Ltd
    BJOG 89 (1982), S. 0 
    Details
    ISSN: 1471-0528
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Medicine
    Notes: Summary. Over a 6 year period, 67 women had a translocated intrauterine contraceptive device (IUCD) removed from the peritoneal cavity or uterovesical fold under general anaesthesia. In 40 patients removal of the IUCD at laparoscopy succeeded, whereas in 24 laparotomy proved necessary and three IUCD were removed per vaginam. Compared with the inert plastic device a larger proportion of copper-containing IUCD in the peritoneal cavity required laparotomy for removal, however, 44% could be removed by laparoscopy, the less traumatic procedure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1471-0528.1982.tb04686.x
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  • 4
    Electronic Resource
    Electronic Resource
    Multiple Solitary Waves Due to Second-Harmonic Generation in Quadratic Media (1999)
    Springer
    Journal of nonlinear science 9 (1999), S. 33-52 
    Details
    ISSN: 1432-1467
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Summary. A detailed mathematical analysis is undertaken of solitary-wave solutions of a system of coupled nonlinear Schrödinger equations describing second-harmonic generation in optical materials with χ (2) nonlinearity. The so-called bright-bright case is studied exclusively. The system depends on a single dimensionless parameter α that includes both wave and material properties. Using methods from the calculus of variations, the first rigorous mathematical proof is given that at least one solitary wave exists for all positive α . Recently, bound states (multipulsed solitary waves) have been found numerically. Using numerical continuation, the region of existence of these solutions is revealed to be α ∈ (0,1), and the bifurcations occurring at the two extremes of this interval are uncovered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s003329900063
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  • 5
    Electronic Resource
    Electronic Resource
    Existence and stability of large scale nonlinear oscillations in suspension bridges (1989)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 40 (1989), S. 172-200 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A nonlinear model of a suspension bridge is considered in which large-scale, stable oscillatory motions can be produced by constant loading and a small-scale, external oscillatory force. Loud's implicit-function theoretic method for determining existence and stability of periodic solutions or nonlinear differential equations is extended to a case of a non-differentiable nonlinearity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00944997
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  • 6
    Electronic Resource
    Electronic Resource
    Nonlinear oscillations in a suspension bridge (1987)
    Springer
    Archive for rational mechanics and analysis 98 (1987), S. 167-177 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00251232
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  • 7
    Electronic Resource
    Electronic Resource
    Multiplicity results for asymptotically homogeneous semilinear boundary value problems (1986)
    Springer
    Annali di matematica pura ed applicata 143 (1986), S. 247-257 
    Details
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper treats nonlinear elliptic boundary value problems of the form $$\Delta u + f(x,u) = 0in\Omega ,u = 0on\partial \Omega $$ in the spaceL 2(Ω) by degree theoretic methods. Emphasis is placed on existence of multiplesolutions in the case, where the nonlinearity f crosses several eigenvalues of the correspondingeigenvalue problem Δθ+λθ = 0 with zero boundary values. No differentiability conditions(but Lipschitz type conditions) on f are assumed. A main tool is a new a priori bound forsolutions (Theorem 1). The method is not confined to the selfadjoint case. It applies alsoto some time-periodic parabolic and hyperbolic problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01769219
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  • 8
    Electronic Resource
    Electronic Resource
    Non-linear flexings in a periodically forced floating beam (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 1-33 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper considers periodic flexing in a floating beam, in the presence of a small periodic forcing term. The beam is considered as a vibrating beam with the free-end boundary condition, in the presence of an additional restoring force due to flotation, which becomes zero as soon as the beam lifts out of the water. The equation is therefore non-linear. A theorem is proved which shows that in the presence of small periodic forcing terms, both small- and large-amplitude solutions can exist. Numerical evidence is presented, which shows that the large-amplitude solutions are stable over a wide range of frequency and amplitude, and suggests a cusp-like surface for the multiple solutions.
    Additional Material: 24 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670140102
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