1 - 10 of 12 articles
We consider systems of nonautonomous nonlinear differential equations with infinite delay. We introduce Carathéodory type conditions for the right-hand side in an equation, which permit one, on the one hand, to cover a fairly broad class of systems and, on the other hand, include the right-hand...
We obtain existence conditions and asymptotic, as t → ω (ω ≤ +∞), representations of a certain class of monotone solutions of an nth-order differential equation whose right-hand side is a sum of terms with regularly varying nonlinearities.
We give definitions of generalized lower and upper functions and generalized solution, which differs from a solution in the conventional sense in that the derivative of a generalized solution can be equal to +∞ and −∞. We show how to use generalized solutions for obtaining classical results.
We consider a bisingular initial value problem for a system of ordinary differential equations with a single small parameter, the asymptotics of whose solution can be constructed in the form of power-logarithmic series on several boundary layers and an external layer. To use the method of...
We consider the Sturm-Liouville operator L(y) = −d
2 + q(x)y in the space L
2[0, π], where the potential q(x) is a complex-valued distribution of the first order of singularity; i.e., q(x) = u′(x), u ∈ L
2[0, π]. (Here the derivative is understood in the sense of distributions.) We obtain...
Under the assumption that the variables in the wave equation can be separated and its coefficients are periodic, we develop a classification of seismic eigenwaves and use it to answer some questions as to how to specify the type and basic parameters of a wave on the basis of measurements of...
We prove the existence and uniqueness of global weak solutions on the entire interval for the Cauchy problem for hyperbolic differential-operator equations with time-discontinuous operators that have variable domains and satisfy certain matching conditions at the points of discontinuity. To this...
For the Gellerstedt equation with a singular coefficient, we study the well-posedness of the problem with the Bitsadze-Samarskii conditions on the ellipticity boundary and on a segment of the degeneration line and with a shift condition on parts of boundary characteristics. We use the maximum...
We construct asymptotic expansions of solutions of the Cauchy problem with rapidly oscillating initial data for hyperbolic systems with constant coefficients and with characteristics of a variable multiplicity. By way of example, we consider the system of Maxwell equations.
For a string vibration process described by an inhomogeneous wave equation, we consider the problem of boundary control at one end of the string with the other end being fixed. For any time interval T > 2l, where l is the string length, we find a function u(0, t) = µ(t) bringing the vibration...
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