All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 9 Next

Displaying 161 – 180 of 327

Showing per page

Admissibly integral manifolds for semilinear evolution equations

Nguyen Thieu Huy, Vu Thi Ngoc Ha (2014)

Annales Polonici Mathematici

We prove the existence of integral (stable, unstable, center) manifolds of admissible classes for the solutions to the semilinear integral equation u ( t ) = U ( t , s ) u ( s ) + ∫ s t U ( t , ξ ) f ( ξ , u ( ξ ) ) d ξ when the evolution family ( U ( t , s ) ) t ≥ s has an exponential trichotomy on a half-line or on the whole line, and the nonlinear forcing term f satisfies the (local or global) φ-Lipschitz conditions, i.e., ||f(t,x)-f(t,y)|| ≤ φ(t)||x-y|| where φ(t) belongs to some classes of admissible function spaces. These manifolds are formed by trajectories of the solutions belonging...

Affine invariant conditions for the topological distinction of quadratic systems with a critical point of the 4th multiplicity.

Mark Voldman, Iu. T. Calin, Nicolae I. Vulpe (1996)

Publicacions Matemàtiques

The affine invariant partition of the set of quadratic systems with one finite singular point of the 4th multiplicity with respect to different topological classes is accomplished. The conditions corresponding to this partition are semi-algebraic, i.e. they are expressed as equalities or inequalities between polynomials.

Algebraic integrability for minimum energy curves

Ivan Yudin, Fátima Silva Leite (2015)

Kybernetika

This paper deals with integrability issues of the Euler-Lagrange equations associated to a variational problem, where the energy function depends on acceleration and drag. Although the motivation came from applications to path planning of underwater robot manipulators, the approach is rather theoretical and the main difficulties result from the fact that the power needed to push an object through a fluid increases as the cube of its speed.

Almost homoclinic solutions for a certain class of mixed type functional differential equations

Joanna Janczewska (2011)

Annales Polonici Mathematici

We shall be concerned with the existence of almost homoclinic solutions for a class of second order functional differential equations of mixed type: q ̈ ( t ) + V q ( t , q ( t ) ) + u ( t , q ( t ) , q ( t - T ) , q ( t + T ) ) = f ( t ) , where t ∈ ℝ, q ∈ ℝⁿ and T>0 is a fixed positive number. By an almost homoclinic solution (to 0) we mean one that joins 0 to itself and q ≡ 0 may not be a stationary point. We assume that V and u are T-periodic with respect to the time variable, V is C¹-smooth and u is continuous. Moreover, f is non-zero, bounded, continuous and square-integrable....

Almost periodic and strongly stable semigroups of operators

Vũ Phóng (1997)

Banach Center Publications

This paper is chiefly a survey of results obtained in recent years on the asymptotic behaviour of semigroups of bounded linear operators on a Banach space. From our general point of view, discrete families of operators T n : n = 0 , 1 , . . . on a Banach space X (discrete one-parameter semigroups), one-parameter C 0 -semigroups T ( t ) : t ≥ 0 on X (strongly continuous one-parameter semigroups), are particular cases of representations of topological abelian semigroups. Namely, given a topological abelian semigroup S, a family of bounded...

Almost periodic generalized solutions of differential equations

Chikh Bouzar, Fethia Ouikene (2021)

Mathematica Bohemica

The paper aims to study systems of linear ordinary differential equations in the context of an algebra of almost periodic generalized ultradistributions. Conditions on the existence of generalized solutions are given.

Currently displaying 161 – 180 of 327