O použití distribucí v teorii lineárních dynamických soustav
O systémech lineárních integrodiferencialních rovnic v technických problémech
O výpočtu pravděpodobností, které se vztahují k časovému vývoji soustav
On a 3D-Hypersingular Equation of a Problem for a Crack
MSC 2010: 45DB05, 45E05, 78A45We show that a certain axisymmetric hypersingular integral equation arising in problems of cracks in the elasticity theory may be explicitly solved in the case where the crack occupies a plane circle. We give three different forms of the resolving formula. Two of them involve regular kernels, while the third one involves a singular kernel, but requires less regularity assumptions on the the right-hand side of the equation.
On a Caginalp phase-field system with a logarithmic nonlinearity
We consider a phase field system based on the Maxwell Cattaneo heat conduction law, with a logarithmic nonlinearity, associated with Dirichlet boundary conditions. In particular, we prove, in one and two space dimensions, the existence of a solution which is strictly separated from the singularities of the nonlinear term and that the problem possesses a finite-dimensional global attractor in terms of exponential attractors.
On a certain integral equation
On a certain nonlinear equation
On a certain non-linear initial-boundary value problem for integro-differential equations of parabolic type
On a certain Volterra-Fredholm type integral equation.
On a class of diffeomorphisms defined by integro-differential operators
We study an integro-differential operator Φ: H̅¹ → L² of Fredholm type and give sufficient conditions for Φ to be a diffeomorphism. An application to functional equations is presented.
On a Class of Fractional Type Integral Equations in Variable Exponent Spaces
2000 Mathematics Subject Classification: 45A05, 45B05, 45E05,45P05, 46E30We obtain a criterion of Fredholmness and formula for the Fredholm index of a certain class of one-dimensional integral operators M with a weak singularity in the kernel, from the variable exponent Lebesgue space L^p(·) ([a, b], ?) to the Sobolev type space L^α,p(·) ([a, b], ?) of fractional smoothness. We also give formulas of closed form solutions ϕ ∈ L^p(·) of the 1st kind integral equation M0ϕ = f, known as the generalized...
On a Class of Hammerstein Integral Equations.
On a class of multivalued variational inequalities.
On a class of nonlinear integral equations arising in neutron transport.
On a class of parabolic integro-differential equations.
On a Class of Retarded Partial Differential Equations.
On a class of second order integrodifferential equations
On a differential game of evasion described by a class of nonlinear Volterra integrodifferential equations
On a fixed point theorem of Krasnoselskii-Schaefer type.
On a Fokker-Planck equation arising in population dynamics.