A construction of equivariant maps based on factorization through symmetric powers of a faithful representation is presented together with several examples of related equivariant maps. Applications to differential equations are also discussed.
We establish several results concerning the asymptotic behavior of random infinite products of generic sequences of affine uniformly continuous operators on bounded closed convex subsets of a Banach space. In addition to weak ergodic theorems we also obtain convergence to a unique common fixed point and more generally, to an affine retraction.
We consider a class of dynamic discrete-time two-player zero-sum games. We show that for a generic cost function and each initial state, there exists a pair of overtaking equilibria strategies over an infinite horizon. We also establish that for a generic cost function f, there exists a pair of stationary equilibria strategies (xf,yf) such that each pair of “approximate...
Let G be a semitopological semigroup, C a nonempty subset of a real Hilbert space H, and ℑ={Tt:t∈G} a representation of G as asymptotically nonexpansive type mappings of C into itself. Let L(x)={z∈H:infs∈Gsupt∈G‖Tts x−z‖=inft∈G‖Tt x−z‖} for each x∈C and L(ℑ)=∩x∈C L(x). In this paper, we prove that ∩s∈Gconv¯{Tts x:t∈G}∩L(ℑ) is nonempty for each x∈C if and only if there exists a...
We obtain new A-properness results for demicontinuous, dissipative type mappings defined only on closed convex subsets of a Banach space X with uniformly convex dual and which satisfy a property called weakly inward. The method relies on a new property of the duality mapping in such spaces. New fixed point results are obtained by utilising a theory of fixed point index.
We establish the global existence of mild solutions to a class of nonlocal Cauchy problems associated with semilinear Volterra integrodifferential equations in a Banach space.
We introduce a new construction of topological degree for densely defined mappings of monotone type. We also study the structure of the classes of mappings involved. Using the basic properties of the degree, we prove some abstract existence results that can be applied to elliptic problems.
We study semilinear elliptic boundary value problems of one parameter dependence where the number of positive solutions is discussed. Our main purpose is to characterize the critical value given by the infimum of such parameters for which positive solutions exist. Our approach is based on super- and sub-solutions, and relies on the topological degree theory on the positive cones...
We consider Borel measures on a locally compact Hausdorff space whose values are linear functionals on a locally convex cone. We define integrals for cone-valued functions and verify that continuous linear functionals on certain spaces of continuous cone-valued functions endowed with an inductive limit topology may be represented by such integrals.
We obtain nontrivial solutions for semilinear elliptic boundary value problems having resonance both at zero and at infinity, when the nonlinear term has asymptotic limits.
On the basis of G-convergence we prove an averaging result for nonlinear abstract parabolic equations, the operator coefficient of which is a stationary stochastic process.
The aim of this paper is to show an application of the recently introduced B-bounded semigroups in the theory of implicit and degenerate evolution equations. The most interesting feature of this approach is its applicability to problems with noncloseable operators.
In 1988, Parker and Sochacki announced a theorem which proved that the Picard iteration, properly modified, generates the Taylor series solution to any ordinary differential equation (ODE) on ℜn with a polynomial generator. In this paper, we present an analogous theorem for partial differential equations (PDEs) with polynomial generators and analytic initial conditions. Since the...
We consider the nonlinear second order conjugate eigenvalue problem on a time scale: y ΔΔ(t)
We study the problem of existence of positive, spherically symmetric strong solutions of quasilinear elliptic equations involving p-Laplacian in the ball. We allow simultaneous strong dependence of the right-hand side on both the unknown function and its gradient. The elliptic problem is studied by relating it to the corresponding singular ordinary integro-differential equation...
We study two one-dimensional equations: the strongly damped wave equation and the heat equation, both with mixed boundary conditions. We prove the existence of global strong solutions and the existence of compact global attractors for these equations in two different spaces.
We study size-structured population models of general type which have the growth rate depending on the size and time. The local existence and uniqueness of the solution have been shown by Kato and Torikata (1997). Here, we discuss the positivity of the solution and global existence as well as L ∞ solutions.
The integration with respect to a vector measure may be applied in order to approximate a function in a Hilbert space by means of a finite orthogonal sequence {fi} attending to two different error criterions. In particular, if Ω∈ℝ is a Lebesgue measurable set, f∈L2(Ω), and {Ai} is a finite family of disjoint subsets of Ω, we can obtain a measure μ0 and an approximation f0...
We consider the one-parameter family of linear operators that A. Belleni Morante recently introduced and called B-bounded semigroups. We first determine all the properties possessed by a couple (A,B) of operators if they generate a B-bounded semigroup (Y(t))t≥0. Then we determine the simplest further property of the couple (A,B) which can assure the existence of a C0-semigroup (T...
We give several examples of Douglas algebras that do not have any maximal subalgebra. We find a condition on these algebras that guarantees that some do not have any minimal superalgebra. We also show that if A is the only maximal subalgebra of a Douglas algebra B, then the algebra A does not have any maximal subalgebra.
We modify the definition of lopsided convergence of bivariate functionals to obtain stability results for the min/sup points of some control problems. In particular, we develop a scheme of finite dimensional approximations to a large class of non-convex control problems.
The initial value problem for hyperbolic equations d 2u(t)/dt 2