Abstract superposition operators on mappings of bounded variation of two real variables. II.
Chistyakov, V.V. (2005)
Sibirskij Matematicheskij Zhurnal
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Chistyakov, V.V. (2005)
Sibirskij Matematicheskij Zhurnal
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Jan Bochenek (1991)
Annales Polonici Mathematici
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By using the theory of strongly continuous cosine families of linear operators in Banach space the existence of solutions of a semilinear second order differential initial value problem (1) as well as the existence of solutions of the linear inhomogeneous problem corresponding to (1) are proved. The main result of the paper is contained in Theorem 5.
Korobkov, M.V. (2000)
Siberian Mathematical Journal
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Xue Zhiqun (2006)
Kragujevac Journal of Mathematics
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Alimohammady, M., Shahmari, A. (2009)
The Journal of Nonlinear Sciences and its Applications
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Korobkov, M.V. (2002)
Sibirskij Matematicheskij Zhurnal
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Stepanov, V.D., Ushakova, E.P. (2010)
Banach Journal of Mathematical Analysis [electronic only]
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Guedda, L., Hallouz, A. (2008)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Penot, Jean-Paul, Zălinescu, Constantin (2000)
Journal of Convex Analysis
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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.
Gutman, A.E., Lisovskaya, S.A. (2009)
Sibirskij Matematicheskij Zhurnal
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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.
V. Bernik (1996)
Acta Arithmetica
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Yakymiv, A.L. (2006)
Publications de l'Institut Mathématique. Nouvelle Série
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