Results 221 to 230 of about 21,792 (245)

Evolution equations with Gel’fond-Leont’ev generalized differentiation operators: II

Differential Equations, 2008
The properties of Gel’fond-Leont’ev generalized differentiation operators in spaces of type W are studied. Conditions are found under which Gel’fond-Leont’ev generalized differentiation operators of infinite order are defined and continuous in spaces of type W.
V. V. Gorodetskii, N. M. Shevchuk
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ON SOME DIFFERENTIAL-OPERATOR EQUATIONS OF ARBITRARY ORDER

Mathematics of the USSR-Sbornik, 1973
On the half-line we investigate the following equation in a Banach space: (1)where are closed operators which commute with . We consider the following classes of equations: parabolic, inverse parabolic, hyperbolic, quasi-elliptic, and quasi-hyperbolic. We present boundary value problems for these classes and prove that they are well-posed. The proofs
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Almost-periodic solutions of differential-operator equations

Siberian Mathematical Journal, 1984
In the paper is proposed a simple method which enables to obtain sufficient conditions for the existence of various classes of almost- periodic solutions of the equations of the type \(P(d/dt)u=\sum^{m}_{k=0}A_ kd^ ku/dt^ k=f,\) \(t\in {\mathbb{R}}\), where \(A_ k\in L(D,X)\) and f is an almost periodic function with values in the Banach space X.
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Differential operators determining solutions of Elliptic equations

Ukrainian Mathematical Journal, 1995
We construct differential operatorsLg(z), Kg(z), Nf¯(z), Mf¯z) which map arbitrary functions holomorphic in a simply connected domainD of the planez=x+iy into regular solutions of the equation $$W_{z\bar z} + A(z,\bar z)W_{\bar z} + B(z,\bar z)W = 0$$ and present examples of the application of these differential operators to the solution of ...
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Differential operator multiplication method for fractional differential equations

Computational Mechanics, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tang, Shaoqiang, Ying, Yuping, Lian, Yanping, Lin, Stephen, Yang, Yibo, Wagner, Gregory J., Liu, Wing Kam   +6 more
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Constitutive Equations in Differential Operator Form

2013
The mechanical response of a viscoelastic material to external loads combines the characteristics of elastic and viscous behavior. On the other hand, as we know from experience, springs and dashpots are mechanical devices which exhibit purely elastic and purely viscous response, respectively. It is then natural to imagine that the equations that relate
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Degenerate differential-operator equations on infinite intervals

Journal of Mathematical Sciences, 2013
In this paper, we define the weighted Sobolev space and the generalized solution of the Dirichlet problem for the one-dimensional equation $$ Lu\equiv {{\left( {-1} \right)}^m}{{\left( {{t^{\alpha }}{u^{(m) }}} \right)}^{(m) }}+A{t^{\beta }}u=f(t).
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Differential Operator Equations in Weighted Sobolev Spaces

1999
In this chapter we consider the ordinary differential equation with constant operator coefficients $$A({D_t})u = fon\mathbb{R}$$ (2.1) .
Vladimir Kozlov, Vladimir Maz’ya
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Constructive foundations of real equations with differential operator

Modeling of systems and processes, 2014
Substantive foundations are offered for solution of differential equations with fixed elements of coefficient system and continuous measurable functions of the right part.
P. Kotov, null Котов
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A Boundary Value Problem for Elliptic Differential-Operator Equations

Results in Mathematics, 2000
The basic part of this article deals with boundary value problems of the type \[ -u''(x)+ Au(x)= f(x),\quad -(A_{\nu 0}u(x))''+ A_{\nu 1}u(x)= f_\nu(x),\quad \nu= 1,\dots, s, \] \[ \alpha_k u^{(p_k)}(0)+ \beta_ku^{(p_k)}u(1)+ \sum^{N_k}_{j= 1} \delta_{kj} u(x_{kj})= 0,\quad k= 1,2, \] with \(x\in [0,1]\), \(p_k\in \{0,1\}\), \(x_{kj}\in [0,1]\); \(A ...
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