Results 251 to 260 of about 1,287,488 (289)

Explicity resolvable equations with functional non‐linearities

Mathematical Methods in the Applied Sciences, 1988
AbstractWe consider the non‐linear evolution equation μdu/dt+Bu+n(u)L(u)=h, where n(u) is a functional, and introduce assumptions which allow its explicit solution. Several concrete applications of our procedure are given.
Bazley, Norman W., Weyer, Jürgen
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Integrability of Resolvents of Systems of Volterra Equations

SIAM Journal on Mathematical Analysis, 1981
The integrability of the resolvents of systems of Volterra integral and integrodifferential equations is studied. The matrix kernels in the equations need not be integrable, and some of the conditions used are shown to be both necessary and sufficient.
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On a Resolvent Estimate of the Stokes Equation on an Infinite Layer

Journal of the Mathematical Society of Japan, 2003
The authors establish the weak solvability of the title problem, and prove standard \(L_p\) estimates for the solution. The proof is based on a partial Fourier transform which reduces the original problem to a two-point boundary value problem for a system of ordinary differential equations with parameter.
ABE, Takayuki, SHIBATA, Yoshihiro
exaly   +3 more sources

On the Asymptotic Behavior of Resolvents of Volterra Equations

SIAM Journal on Mathematical Analysis, 1980
This paper considers the asymptotic behavior of the resolvent r of the Volterra equation \[(1)\qquad x(t) + \int_0^t {a(t - s)x(s)ds = f(t),\quad t \geqq 0} \] given by \[(2)\qquad r(t) + \int_0^t {a(t - s)r(s)ds = a(t),\quad t \geqq 0.} \] Both integrability and pointwise estimates for r are established and some of these are shown to be uniform with ...
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The resolvent approach for the wave equation

Computational Mathematics and Mathematical Physics, 2015
Actually there is an improvement of an earlier technique developed by \textit{A. N. Krylov} [On some differential equations of mathematical physics having applications in engineering (Russian). Moskva-Leningrad: Gostekhteorixdat (1950)] and \textit{V. A.
Burlutskaya, M. Sh., Khromov, A. P.
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Fixed Points, Volterra Equations, and Becker’s Resolvent

Acta Mathematica Hungarica, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
T A Burton
exaly   +3 more sources

The Method of Resolvent Equations

1987
Generally speaking, the perturbation theory which forms the heart of theoretical methods for treating off-resonant phenomena cannot be applied directly in the case of resonant multiphoton processes. Modifications are called for to correctly and conveniently approach the problem of resonance breakdown of ordinary perturbation theory. This is most easily
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Equations in βG and the resolvability of abelian groups

Mathematical Notes, 1999
In this paper, the author continues his study of resolvability in Abelian groups with some weak continuity assumptions. A space is called resolvable (resp. \(\omega\)-resolvable) if it can be decomposed into two (countably many) dense subsets. A typical result says: let \(G\) be an Abelian group with a nondiscrete topology such that all translations ...
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Resolvent Formulas for a Volterra Equation in Hilbert Space

SIAM Journal on Mathematical Analysis, 1982
Let ${\bf y}(t,{\bf x},{\bf f})$ denote the solution of the Cauchy problem \[ {\bf y}'(t) + \int_0^t {[d + a(t - s)]{\bf Ly}(s)ds = {\bf f}(t),\quad t \geqq 0,\quad {\bf y}(0) = {\bf x},} \] where $d \geqq 0$ and ${\bf L}$ is a self-adjoint densely defined linear operator on a Hilbert space $\mathcal{H}$ with ${\bf L} \geqq \lambda _1 {\bf I}$.
Carr, Ralph W., Hannsgen, Kenneth B.
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Fredholm resolvents, Wiener-Hopf equations, and Riccati differential equations

IEEE Transactions on Information Theory, 1969
We shall show that the solution of Fredholm equations with symmetric kernels of a certain type can be reduced to the solution of a related Wiener-Hopf integral equation. A least-squares filtering problem is associated with this equation. When the kernel has a separable form, this related problem suggests that the solution can be obtained via a matrix ...
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