Jan Bochenek (1999)
Annales Polonici Mathematici
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This paper is devoted to the investigation of the abstract semilinear initial value problem du/dt + A(t)u = f(t,u), u(0) = u₀, in the "parabolic" case.
Appleby, John A.D., Reynolds, David W. (2003)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Vanualailai, Jito (2002)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Messaoudi, Salim A. (2005)
Abstract and Applied Analysis
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Belmekki, M., Benchohra, M., Ntouyas, S.K. (2006)
Fixed Point Theory and Applications [electronic only]
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Purnaras, I.K. (2007)
Electronic Journal of Qualitative Theory of Differential Equations [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.
Burton, T.A. (2008)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Berroug, Tarik (2010)
Applied Mathematics E-Notes [electronic only]
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S. Mazouzi, Nasser-eddine Tatar (2003)
Archivum Mathematicum
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We prove exponential decay for the solution of an abstract integrodifferential equation. This equation involves coefficients of polynomial type, weakly singular kernels as well as different powers of the unknown in some norms.