Symmetry and concentration behavior of ground state in axially symmetric domains.
Symmetry and monotonicity of solutions to some variational problems in cylinders and annuli.
Syntheses of differential games and pseudo-Riccati equations.
System of general variational inequalities involving different nonlinear operators related to fixed point problems and its applications.
System of generalized implicit vector quasivariational inequalities.
Systems of reaction-diffusion equations with spatially distributed hysteresis
We study systems of reaction-diffusion equations with discontinuous spatially distributed hysteresis on the right-hand side. The input of the hysteresis is given by a vector-valued function of space and time. Such systems describe hysteretic interaction of non-diffusive (bacteria, cells, etc.) and diffusive (nutrient, proteins, etc.) substances leading to formation of spatial patterns. We provide sufficient conditions under which the problem is well posed in spite of the assumed discontinuity of...
Systems with hysteresis in the feedback loop : existence, regularity and asymptotic behaviour of solutions
An existence and regularity theorem is proved for integral equations of convolution type which contain hysteresis nonlinearities. On the basis of this result, frequency-domain stability criteria are derived for feedback systems with a linear infinite-dimensional system in the forward path and a hysteresis nonlinearity in the feedback path. These stability criteria are reminiscent of the classical circle criterion which applies to static sector-bounded nonlinearities. The class of hysteresis operators...
Systems with hysteresis in the feedback loop: existence, regularity and asymptotic behaviour of solutions
An existence and regularity theorem is proved for integral equations of convolution type which contain hysteresis nonlinearities. On the basis of this result, frequency-domain stability criteria are derived for feedback systems with a linear infinite-dimensional system in the forward path and a hysteresis nonlinearity in the feedback path. These stability criteria are reminiscent of the classical circle criterion which applies to static sector-bounded nonlinearities. The class of hysteresis operators...
The aftermath of the intermediate value theorem.
The Approximation of Generalized Turning Points by Projection Methods with Superconvergence to the Critical Parameter.
The Cauchy problem for the nonlinear Schrödinger Equation in H1.
The coincidence index for fundamentally contractible multivalued maps with nonconvex values
We study a coincidence problem of the form A(x) ∈ ϕ (x), where A is a linear Fredholm operator with nonnegative index between Banach spaces and ϕ is a multivalued A-fundamentally contractible map (in particular, it is not necessarily compact). The main tool is a coincidence index, which becomes the well known Leray-Schauder fixed point index when A=id and ϕ is a compact singlevalued map. An application to boundary value problems for differential equations in Banach spaces is given.
The comparison of the convergence speed between Picard, Mann, Krasnoselskij and Ishikawa iterations in Banach spaces.
The concentration-compactness principle in the calculus of variations. The locally compact case, part 1
The convergence of an implicit mean value iteration.
The convergence of mean value iteration for a family of maps.
The Dependence of Critical Parameter Bounds on the Monotonicity of a Newton Sequence.
The effect of rounding errors on a certain class of iterative methods
In this study we are concerned with the problem of approximating a solution of a nonlinear equation in Banach space using Newton-like methods. Due to rounding errors the sequence of iterates generated on a computer differs from the sequence produced in theory. Using Lipschitz-type hypotheses on the mth Fréchet derivative (m ≥ 2 an integer) instead of the first one, we provide sufficient convergence conditions for the inexact Newton-like method that is actually generated on the computer. Moreover,...
The eigenvalue problem for a singular quasilinear elliptic equation.
The equivalence between -stabilities of the Krasnoselskij and the Mann iterations.