Continuous dependence of solutions in magneto-elasticity theory.
Bofill, F., Quintanilla, R. (2003)
International Journal of Mathematics and Mathematical Sciences
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Bofill, F., Quintanilla, R. (2003)
International Journal of Mathematics and Mathematical Sciences
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Ibrahim, Sobhy El-Sayed (2003)
International Journal of Mathematics and Mathematical Sciences
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Frota, C.L., Lar'kin, N.A. (1998)
Portugaliae Mathematica
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S. Staněk (1992)
Annales Polonici Mathematici
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A differential equation of the form (q(t)k(u)u')' = λf(t)h(u)u' depending on the positive parameter λ is considered and nonnegative solutions u such that u(0) = 0, u(t) > 0 for t > 0 are studied. Some theorems about the existence, uniqueness and boundedness of solutions are given.
Burton, T.A. (2008)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Purnaras, I.K. (2007)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Islam, M., Neugebauer, J.T. (2008)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Bahlali, K., Elouaflin, A., N'zi, M. (2004)
Journal of Applied Mathematics and Stochastic Analysis
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Ngoc, Le Thi Phuong, Long, Nguyen Thanh (2006)
Fixed Point Theory and Applications [electronic only]
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Svatoslav Staněk (1995)
Annales Polonici Mathematici
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The differential equation of the form , a ∈ (0,∞), is considered and solutions u with u(0) = 0 and (u(t))² + (u’(t))² > 0 on (0,∞) are studied. Theorems about existence, uniqueness, boundedness and dependence of solutions on a parameter are given.
Alexander Lomtatidze, Jiří Šremr (2012)
Czechoslovak Mathematical Journal
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We study the question of the existence, uniqueness, and continuous dependence on parameters of the Carathéodory solutions to the Cauchy problem for linear partial functional-differential equations of hyperbolic type. A theorem on the Fredholm alternative is also proved. The results obtained are new even in the case of equations without argument deviations, because we do not suppose absolute continuity of the function the Cauchy problem is prescribed on, which is rather usual assumption...