Stability, boundedness and asymptotic behaviour of solutions of certain nonlinear differential equations of the third order
A. T. Ademola, P. O. Arawomo (2011)
Kragujevac Journal of Mathematics
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A. T. Ademola, P. O. Arawomo (2011)
Kragujevac Journal of Mathematics
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Cecchi, Mariella, Došlá, Zuzana, Marini, Mauro (2000)
Georgian Mathematical Journal
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Vlamos, Panayiotis (2001)
International Journal of Mathematics and Mathematical Sciences
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Olaru, Marian, Olaru, Vasilica (2006)
General Mathematics
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Jangveladze, T., Kiguradze, Z. (2002)
Georgian Mathematical Journal
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Jaromír J. Koliha, Ivan Straškraba (1997)
Commentationes Mathematicae Universitatis Carolinae
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The stabilization of solutions to an abstract differential equation is investigated. The initial value problem is considered in the form of an integral equation. The equation is solved by means of the Banach contraction mapping theorem or the Schauder fixed point theorem in the space of functions decreasing to zero at an appropriate rate. Stable manifolds for singular perturbation problems are compared with each other. A possible application is illustrated on an initial-boundary-value...
Raffoul, Youssef N. (2009)
Banach Journal of Mathematical Analysis [electronic only]
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Svatoslav Staněk (1993)
Annales Polonici Mathematici
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A differential equation of the form (q(t)k(u)u')' = F(t,u)u' is considered and solutions u with u(0) = 0 are studied on the halfline [0,∞). Theorems about the existence, uniqueness, boundedness and dependence of solutions on a parameter are given.
Bartušek, Miroslav (2006)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Xingbao Wu (1995)
Annales Polonici Mathematici
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A nonlinear differential equation of the form (q(x)k(x)u')' = F(x,u,u') arising in models of infiltration of water is considered, together with the corresponding differential equation with a positive parameter λ, (q(x)k(x)u')' = λF(x,u,u'). The theorems about existence, uniqueness, boundedness of solution and its dependence on the parameter are established.