Singular Integral Equations with Monotone Nonlinearity in Complex Lebesgue Spaces

Stochastic evolution equations with multiplicative Poisson noise and monotone nonlinearity

Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift in Hilbert spaces are considered‎. ‎The coefficients are assumed to have linear growth‎. ‎We do not impose coercivity conditions on coefficients‎. ‎A novel method of proof for establishing existence and uniqueness of the mild solution is proposed‎. ‎Examples on stochastic partial differentia...

Direct methods for solving singular integral equations with complex conjugation

The computational schemes of collocation and mechanical quadrature methods for solving singular integral equations (S.I.E.) containing the complex conjugate unknown function are proposed in this paper. A theoretical foundation of these two methods is obtained in Hölder functions space Hβ (0 < β < 1) and in Lp, 1 < p < ∞ spaces. A rather common case of a nonstandard contour of integration is inv...

On approximate solution of non-elliptic singular integral equation systems in Lebesgue spaces

We investigate in this paper problems of theoretical foundation of collocations and mechanical quadratures methods for approximate solution of singular integral equation systems in the case, when their symbols have on the integration contour a finite set of integer degree zeroes. We consider the case when equation digitalization points are taken in such a way that each point of the contour can ...

Continuous dependence on coefficients for stochastic evolution equations with multiplicative Levy Noise and monotone nonlinearity

Semilinear stochastic evolution equations with multiplicative L'evy noise are considered‎. ‎The drift term is assumed to be monotone nonlinear and with linear growth‎. ‎Unlike other similar works‎, ‎we do not impose coercivity conditions on coefficients‎. ‎We establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients. ‎As corollaries of ...

Numerical Solution of Weakly Singular Integrodifferential Equations on Closed Smooth Contour in Lebesgue Spaces