Ray's theorem for firmly nonexpansive-like mappings and equilibrium problems in Banach spaces.
Reaction-diffusion systems: Destabilizing effect of conditions given by inclusions.
Reaction-diffusion systems: Destabilizing effect of conditions given by inclusions
Sufficient conditions for destabilizing effects of certain unilateral boundary conditions and for the existence of bifurcation points for spatial patterns to reaction-diffusion systems of the activator-inhibitor type are proved. The conditions are related with the mollification method employed to overcome difficulties connected with empty interiors of appropriate convex cones.
Reaction-diffusion systems: Destabilizing effect of conditions given by inclusions II, Examples
The destabilizing effect of four different types of multivalued conditions describing the influence of semipermeable membranes or of unilateral inner sources to the reaction-diffusion system is investigated. The validity of the assumptions sufficient for the destabilization which were stated in the first part is verified for these cases. Thus the existence of points at which the spatial patterns bifurcate from trivial solutions is proved.
Realization theory methods for the stability investigation of nonlinear infinite-dimensional input-output systems
Realization theory for linear input-output operators and frequency-domain methods for the solvability of Riccati operator equations are used for the stability and instability investigation of a class of nonlinear Volterra integral equations in a Hilbert space. The key idea is to consider, similar to the Volterra equation, a time-invariant control system generated by an abstract ODE in a weighted Sobolev space, which has the same stability properties as the Volterra equation.
Recenti sviluppi nella teoria del grado topologico
Reflexive Banach space and fixed point theorems.
Reflexivity and approximate fixed points
A Banach space X is reflexive if and only if every bounded sequence xₙ in X contains a norm attaining subsequence. This means that it contains a subsequence for which is attained at some f in the dual unit sphere . A Banach space X is not reflexive if and only if it contains a normalized sequence xₙ with the property that for every , there exists such that . Combining this with a result of Shafrir, we conclude that every infinite-dimensional Banach space contains an unbounded closed convex...
Regular maximal monotone operators and the sum theorem.
Regular Splittings and Monotone Iteration Functions.
Régularisation pour les problèmes à opérateurs monotones et la méthode de Galerkin
Regularity for entropy solutions of parabolic p-Laplacian type equations.
In this note we give some summability results for entropy solutions of the nonlinear parabolic equation ut - div ap (x, ∇u) = f in ] 0,T [xΩ with initial datum in L1(Ω) and assuming Dirichlet's boundary condition, where ap(.,.) is a Carathéodory function satisfying the classical Leray-Lions hypotheses, f ∈ L1 (]0,T[xΩ) and Ω is a domain in RN. We find spaces of type Lr(0,T;Mq(Ω)) containing the entropy solution and its gradient. We also include some summability results when f = 0 and the p-Laplacian...
Regularity of the symbolic calculus in Besov algebras
Regularization and error estimates for nonhomogeneous backward heat problems.
Regularization and new error estimates for a modified Helmholtz equation.
Regularization for evolution equations in Hilbert spaces involving monotone operators via the semi-flows method.
Regularization inertial proximal point algorithm for monotone hemicontinuous mapping and inverse strongly monotone mappings in Hilbert spaces.
Regularization of noncoercive constraints in Hencky plasticity
The aim of this paper is to find the largest lower semicontinuous minorant of the elastic-plastic energy of a body with fissures. The functional of energy considered is not coercive.
Regularization of nonlinear ill-posed equations with accretive operators.
Regularization properties of Tikhonov regularization with sparsity constraints.