On a class of continuous flow.
Mogollon, Ramon (1980)
International Journal of Mathematics and Mathematical Sciences
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Mogollon, Ramon (1980)
International Journal of Mathematics and Mathematical Sciences
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Yuhua Long, Baoling Zeng (2017)
Open Mathematics
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In this paper, we study second-order nonlinear discrete Robin boundary value problem with parameter dependence. Applying invariant sets of descending flow and variational methods, we establish some new sufficient conditions on the existence of sign-changing solutions, positive solutions and negative solutions of the system when the parameter belongs to appropriate intervals. In addition, an example is given to illustrate our results.
Alexander Shnirelman (1999-2000)
Séminaire Équations aux dérivées partielles
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de Vries, Jan, van der Woude, Jaap
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Paul R. Fallone, Jr. (1971)
Czechoslovak Mathematical Journal
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Saroop Kaul (1987)
Fundamenta Mathematicae
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Alexander Shnirelman (1999)
Journées équations aux dérivées partielles
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In the existing stability theory of steady flows of an ideal incompressible fluid, formulated by V. Arnold, the stability is understood as a stability with respect to perturbations with small in vorticity. Nothing has been known about the stability under perturbation with small energy, without any restrictions on vorticity; it was clear that existing methods do not work for this (the most physically reasonable) class of perturbations. We prove that in fact, every nontrivial steady...