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Differential Invariants of Second Order ODEs, I

✍ Scribed by Valeriy A. Yumaguzhin

Publisher
Springer Netherlands
Year
2009
Tongue
English
Weight
768 KB
Volume
109
Category
Article
ISSN
0167-8019

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πŸ“œ SIMILAR VOLUMES

Differential invariants of the one-dimen
Differential invariants of the one-dimensional quasi-linear second-order evolution equation
✍ N.H. Ibragimov; C. Sophocleous πŸ“‚ Article πŸ“… 2007 πŸ› Elsevier Science 🌐 English βš– 237 KB

We consider evolution equations of the form u t = f(x, u, u x )u xx + g(x, u, u x ) and u t = u xx + g(x, u, u x ). In the spirit of the recent work of Ibragimov [Ibragimov NH. Laplace type invariants for parabolic equations. Nonlinear Dynam 2002;28:125-33] who adopted the infinitesimal method for c

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We discuss the existence of positive solutions of the system where the nonlinearities f and g satisfy a superlinearity condition at both 0 and ∞. Our main result is the proof of a priori bounds for the eventual solutions. As an application, we consider the Dirichlet problem in an annulus for system