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In this paper, the classical Lie theory is applied to study the Benjamin-Bona-Mahony (BBM) and modified Benjamin-Bona-Mahony equations (MBBM) to obtain their symmetries, invariant solutions, symmetry reductions and differential invariants. By observation of the the adjoint representation of Mentioned symmetry groups on their Lie algebras, we find the primary classification (optimal system) of their group-invariant solutions which provides new exact solutions to BBM and MBBM equations. Finally, conservation...

Regularly Varying Solutions of Perturbed Euler Differential Equations and Related Functional Differential Equations

Kusano Takasi, Vojislav Marić (2010)

Publications de l'Institut Mathématique

Relationship between different types of stability for linear almost periodic systems in Banach spaces.

Cheban, D.N. (1999)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Remark in connection with an article of G. G. Hamedani: “Global existence of solutions of certain functional-differential equations” [Časopis Pěst. Mat. 106 (1981), 48-51]

Bogdan Rzepecki (1983)

Časopis pro pěstování matematiky

Remark to transformations of functional-differential equations of the first order

Václav Tryhuk (1999)

Mathematica Slovaca

Remark to transformations of linear differential and functional-differential equations

Václav Tryhuk (2000)

Czechoslovak Mathematical Journal

For linear differential and functional-differential equations of the $n$ -th order criteria of equivalence with respect to the pointwise transformation are derived.

Remarks on existence of positive solutions of some integral equations

Jan Ligęza (2005)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

We study the existence of positive solutions of the integral equation $x (t) = μ \int_{0}^{1} k (t, s) f (s, x (s), x^{'} (s), ..., x^{(n - 1)} (s)) d s, n \geq 2$ in both $C^{n - 1} [0, 1]$ and $W^{n - 1, p} [0, 1]$ spaces, where $p \geq 1$ and $μ > 0$ . Throughout this paper $k$ is nonnegative but the nonlinearity $f$ may take negative values. The Krasnosielski fixed point theorem on cone is used.

Remarque sur la stabilité dans le cas d'une équation linéaire à paramètre retardé avec une perturbation non linéaire

Z. Mikołajska (1977)

Annales Polonici Mathematici

Remarque sur une propriété asymptotique des solutions d'une équation différentielle à paramètre retardé

Z. Mikołajska (1983)

Annales Polonici Mathematici

Representation of solutions of linear discrete systems with constant coefficients and pure delay.

Diblík, J., Khusainov, D.Ya. (2006)

Advances in Difference Equations [electronic only]

Resolvent of nonautonomous linear delay functional differential equations

Joël Blot, Mamadou I. Koné (2015)

Nonautonomous Dynamical Systems

The aim of this paper is to give a complete proof of the formula for the resolvent of a nonautonomous linear delay functional differential equations given in the book of Hale and Verduyn Lunel [9] under the assumption alone of the continuity of the right-hand side with respect to the time,when the notion of solution is a differentiable function at each point, which satisfies the equation at each point, and when the initial value is a continuous function.

Retarded Actions on Oscillations

Y. G. Sficas (1976)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

Retarded differential equations by the extrapolation method. (Équations différentielles à retard par la méthode d'extrapolation.)

Maniar, L. (1997)

Portugaliae Mathematica

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