By Steeb W.-H.

ISBN-10: 9810213557

ISBN-13: 9789810213558

The invertible aspect transformation is a strong software within the learn of nonlinear differential and distinction questions. This booklet supplies a complete creation to this system. traditional and partial differential equations are studied with this process. The ebook additionally covers nonlinear distinction equations. The connections with Lie symmetries, the Painleve estate, first integrals and the Cartan equivalence process are mentioned intimately. many of the reviews are checked with the pc language lessen; the ebook comprises 30 decrease courses. a brief advent to the jet package formalism is given

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**Invertible Point Transformations and Nonlinear Differential - download pdf or read online**

The invertible element transformation is a strong device within the research of nonlinear differential and distinction questions. This ebook provides a entire creation to this system. traditional and partial differential equations are studied with this process. The ebook additionally covers nonlinear distinction equations.

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**Extra resources for Invertible Point Transformations and Nonlinear Differential Equations**

**Example text**

Gastaldi and F. Tomarelli, Some remarks on nonlinear noncoercive variaiional inequali ties, BoUettino U. M. I. 7, 1-B (1987), 143-165. [6] J. L. Lions, "Quelques methodes de resolution des problemes limites nonlineaires," Dunod, Paris, 1969. [7] S. Timoshenko, "Theory of Plates and Shells," MacGraw Hill, New York, London, 1940. E IMPLIED BY JUMP DISCONTINUITIES OF THE COEFFICIENTS 0 . ARINO Departement de Mathematiques Universite de PAU 64000 PAU (FRANCE) AND A. BEN M'BAREK Departement de Mathematiques Faculte des Sciences RABAT (MOROCCO) ABSTRACT We c o n s i d e r t h e f o l l o w i n g c l a s s of equations : 2 d y —2 dt dy * H(y, — ) y = g ( y ) , dt where g Is smooth and H(u,v) Is a positive constant on each of the four quadrants determined by the u and v axes.

I. 7, 1-B (1987), 143-165. [6] J. L. Lions, "Quelques methodes de resolution des problemes limites nonlineaires," Dunod, Paris, 1969. [7] S. Timoshenko, "Theory of Plates and Shells," MacGraw Hill, New York, London, 1940. E IMPLIED BY JUMP DISCONTINUITIES OF THE COEFFICIENTS 0 . ARINO Departement de Mathematiques Universite de PAU 64000 PAU (FRANCE) AND A. BEN M'BAREK Departement de Mathematiques Faculte des Sciences RABAT (MOROCCO) ABSTRACT We c o n s i d e r t h e f o l l o w i n g c l a s s of equations : 2 d y —2 dt dy * H(y, — ) y = g ( y ) , dt where g Is smooth and H(u,v) Is a positive constant on each of the four quadrants determined by the u and v axes.

44 It should be clear from the above considerations that not only the problem of existence of periodic solutions can be dealt with by looking at the function w(u) but the stability problem as well. In fact, w Is a Polncare map for equation (1) and carries the relevant information on these questions. Thus, looking at the graph of w, when Proposition 2 applies, we can see that the non trivial periodic solution, when it exists, attracts all the solutions, except zero, at +«o if Q > 1, at -co If Q < 1.

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Categories: Differential Equations