Abstract and Applied Analysis


List of Papers (Total 3,038)

Existence of positive radial solutions for a weakly coupled system via blow up

The existence of positive solutions to certain systems of ordinary differential equations is studied. Particular forms of these systems are satisfied by radial solutions of associated partial differential equations.

Semilinear Volterra integrodifferential equations with nonlocal initial conditions

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.

Asymptotic properties of mild solutions of nonautonomous evolution equations with applications to retarded differential equations

We investigate the asymptotic properties of the inhomogeneous nonautonomous evolution equation (d/dt)u(t)=Au(t)

On boundary value problems for degenerate differential inclusions in Banach spaces

We consider the applications of the theory of condensing set-valued maps, the theory of set-valued linear operators, and the topological degree theory of the existence of mild solutions for a class of degenerate differential inclusions in a reflexive Banach space. Further, these techniques are used to obtain the solvability of general boundary value problems for a given class of...

Positive solutions of some nonlocal boundary value problems

We establish the existence of positive solutions of some m-point boundary value problems under weaker assumptions than previously employed. In particular, we do not require all the parameters occurring in the boundary conditions to be positive. Our results allow more general behaviour for the nonlinear term than being either sub- or superlinear.

An elliptic problem with critical exponent and positive Hardy potential

We give the existence result and the vanishing order of the solution in 0 for the following equation: −Δu(x)

Positive solutions for singular discrete boundary value problems

We study the existence of zero-convergent solutions for the second-order nonlinear difference equation Δ(anΦp(Δxn))=g(n,xn

The generalized Conley index and multiple solutions of semilinear elliptic problems

We establish some framework so that the generalized Conley index can be easily used to study the multiple solution problem of semilinear elliptic boundary value problems. Both the parabolic flow and the gradient flow are used. Some examples are given to compare our approach here with other well-known methods. Our abstract results with parabolic flows may have applications to...

A proximal point method for nonsmooth convex optimization problems in Banach spaces

In this paper we show the weak convergence and stability of the proximal point method when applied to the constrained convex optimization problem in uniformly convex and uniformly smooth Banach spaces. In addition, we establish a nonasymptotic estimate of convergence rate of the sequence of functional values for the unconstrained case. This estimate depends on a geometric...

Uniform asymptotic normal structure, the uniform semi-Opial property and fixed points of asymptotically regular uniformly lipschitzian semigroups. Part I

In this paper we introduce the uniform asymptotic normal structure and the uniform semi-Opial properties of Banach spaces. This part is devoted to a study of the spaces with these properties. We also compare them with those spaces which have uniform normal structure and with spaces with WCS(X)>1.

On the existence of classical solutions for differential-functional IBVP

We consider the initial-boundary value problem for second order differential-functional equations of parabolic type. Functional dependence in the equation is of the Hale type. By using Leray-Schauder theorem we prove the existence of classical solutions. Our formulation and results cover a large class of parabolic problems both with a deviated argument and integro-differential...

Nonlinear ergodic theorems for a semitopological semigroup of non-Lipschitzian mappings without convexity

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...

Semilinear Volterra integrodifferential equations with nonlocal initial conditions

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.

Homoclinic solutions for linear and linearizable ordinary differential equations

Using functional arguments, some existence results for the infinite boundary value problem x˙=F(t,x),x(−∞)=x(

Extension of the best approximation operator in Orlicz spaces and weak-type inequalities

We consider an extension of the best approximation operator from an Orlicz space L φ to the space L φ′, where φ′ denotes the derivative of φ, and we prove a weak-type inequality in this space. Further, we obtain some strong inequalities for suitable L ψ spaces.

On the projection constants of some topological spaces and some applications

We find a lower estimation for the projection constant of the projective tensor product X⊗ ∧Y and the injective tensor product X⊗ ∨Y, we apply this estimation on some previous results, and we also introduce a new concept of the projection constants of operators rather than that defined for Banach spaces.

On projection constant problems and the existence of metric projections in normed spaces

We give the sufficient conditions for the existence of a metric projection onto convex closed subsets of normed linear spaces which are reduced conditions than that in the case of reflexive Banach spaces and we find a general formula for the projections onto the maximal proper subspaces of the classical Banach spaces l p,1≤p<∞ and c 0. We also give the sufficient and necessary...

The integral wavelet transform in weighted Sobolev spaces

The integral wavelet transform is defined in weighted Sobolev spaces, in which some properties of the transform as well as its asymptotical behaviour for small dilation parameter are studied.

Ordinary differential systems describing hysteresis effects and numerical simulations

We consider a general class of ordinary differential systems which describes input-output relations of hysteresis types, for instance, play or stop operators. The system consists of two first-order nonlinear ODEs and one of them includes a subdifferential operator depending on the unknowns. Our main objective of this paper is to give an existence-uniqueness result for the system...

On the modulus of u-convexity of Ji Gao

We consider the modulus of u-convexity of a Banach space introduced by Ji Gao (1996) and we improve a sufficient condition for the fixed-point property (FPP) given by this author. We also give a sufficient condition for normal structure in terms of the modulus of u-convexity.

Attractors of iterated function systems and Markov operators

This paper contains a review of results concerning “generalized” attractors for a large class of iterated function systems {wi:i∈I} acting on a complete separable metric space. This generalization, which originates in the Banach contraction principle, allows us to consider a new class of sets, which we call semi-attractors (or semifractals). These sets have many interesting...