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Norman W. Bazley 《manuscripta mathematica》1976,18(4):353-369
We consider an equation of the form Au+N(u)=u in a Hilbert space and assume that the nonlinearity N is reproducing relative to a known sequence of vectors. Under this assumption the Rayleigh-Ritz-Galerkin approximations lead to a simple class of nonlinear algebraic eigenvalue problems.In a general variational case we show that Lusternik-Schnirelmann critical values of Rayleigh-Ritz-Galerkin problems provide upper bounds to those of the original problem. Lower bounds are constructed in the case N(u)=B*(Bu)3.The author would like to thank the European Research Office for their assistance in this research. 相似文献
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It is shown that results of available theoretical analyses of the far-field sound pressure due to a simple source above an absorbing plane are capable of simple interpretation, and that certain published experimental values of excess attenuation obtained from measurements near the ground are consistent with such results. The effects of changing various parameters are demonstrated and estimates made of the errors likely to be incurred if effects of ground absorption are ignored when determining normalized values of the noise of aircraft. 相似文献
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A nonlinear evolution equation in Hilbert space is introduced and is shown to govern a broad class of problems of nonlinear solid mechanics. The simplest oscillations of this equation are described by a “generalized Liénard equation.” AMS(MOS) Classification Nos: 73D35, 73F15, 58D25, 35L35, 34G20, 34C15. 相似文献
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N. W. Bazley R. J. Weinacht E. de Jager 《Mathematical Methods in the Applied Sciences》1984,6(1):206-214
We treat wave equations with “scalar nonlinearities” and demonstrate the connection between the bifurcation theory of an associated system of Hammerstein integral equations and the existence of periodic solutions of the nonlinear wave equation. 相似文献
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An explicitly resolvable model, which was instroduced in a previous paper (see [1]), is used to obtain exact behaviour of its bifurcation curves. The model closely approximates the true Arrhenius law for a spherical vessel of reacting material undergoing an exothermic reaction in three or more dimensions. For a sequence of values of a parameter, which is the reciprocal of the dimensionless activation energy, the number of the solutions changes for certain values of the eigenparameter Further, there exist solutions for all then is non-zero.
Supported in part by the Deutsche Forschungsgemeinschaft and in part by the Victoria University of Wellington Fellowship Committee. 相似文献
Zusammenfassung Mit Hilfe eines explizit lösbaren Modells, das in einer früheren Arbeit eingeführt wurde (siehe [1]), erhält man das exakte Verhalten der zugehörigen Verzweigungskurven. Das Modell approximiert gut das Arrheniussche Gesetz für exotherme Reaktionen in einem sphärischen Topf in drei oder mehr Dimensionen. Für eine Folge von Werten des Parameters, welches als Reziproke der dimensionslosen Aktivierungsenergie dient, ändert sich die Anzahl der Lösungen zum Eigenwert, der durch gesteuert wird. Weiter gibt es für alle mindestens eine Lösung, sofern 0 gilt.
Supported in part by the Deutsche Forschungsgemeinschaft and in part by the Victoria University of Wellington Fellowship Committee. 相似文献
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Summary We consider a class of simple examples and investigate the connection between the solutions of the nonlinear wave equation and the solutions of the corresponding bifurcation problem.
Research supported in part by the European Research Office of the United States Army. 相似文献
Zusammenfassung An einfachen Klassen von Beispielen wird der Zusammenhang untersucht zwischen den periodischen Lösungen nichtlinearer Wellengleichungen und den Lösungen des zugehörigen Verzweigungsproblems.
Research supported in part by the European Research Office of the United States Army. 相似文献
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Zusammenfassung Es werden Verfahren zur Berechnung der unteren Grenzen des Frequenzgangs freier Schwingungen von kontinuierlichen linear-elastischen Systemen dargestellt. Diese Verfahren beruhen auf einer systematischen Verbesserung der durch explizite Lösung ähnlicher, jedoch einfacherer Schwingungsprobleme hergeleiteten unteren Grenzen. Die Allgemeinheit unserer Darstellung ermöglicht die Erfassung einer umfangreichen Klasse linearer Theorien. Die Anwendbarkeit dieser Verfahren wird an Beispielen aus der klassischen Plattentheorie erläutert, und es werden numerische Ergebnisse für vier Balkenprobleme angegeben.
Sponsored in part by the Aeronautical Research Laboratories, OAR, through the European Office of Aerospace Research, United States Air Force.
Sponsored in part by the Department of the Navy under contract NOw-62-0604-c with the Bureau of Naval Weapons. 相似文献
Sponsored in part by the Aeronautical Research Laboratories, OAR, through the European Office of Aerospace Research, United States Air Force.
Sponsored in part by the Department of the Navy under contract NOw-62-0604-c with the Bureau of Naval Weapons. 相似文献