Fixed points for discontinuous monotone operators.
Fixed points for pseudocontractive mappings on unbounded domains.
Fixed points of discontinuous multivalued operators in ordered spaces with applications.
Floquet boundary value problem of fractional functional differential equations.
Form perturbations of the second quantized Dirac field.
Fourier-like methods for equations with separable variables
It is well known that a power of a right invertible operator is again right invertible, as well as a polynomial in a right invertible operator under appropriate assumptions. However, a linear combination of right invertible operators (in particular, their sum and/or difference) in general is not right invertible. It will be shown how to solve equations with linear combinations of right invertible operators in commutative algebras using properties of logarithmic and antilogarithmic mappings. The...
Fractional BVPs with strong time singularities and the limit properties of their solutions
In the first part, we investigate the singular BVP , u(0) = A, u(1) = B, c D α u(t)|t=0 = 0, where is a continuous operator, α ∈ (0, 1) and a < 0. Here, c D denotes the Caputo fractional derivative. The existence result is proved by the Leray-Schauder nonlinear alternative. The second part establishes the relations between solutions of the sequence of problems , u(0) = A, u(1) = B, where a < 0, 0 < β n ≤ α n < 1, limn→∞ β n = 1, and solutions of u″+(a/t)u′ = f(t, u, u′) satisfying...
Fractional integro-differential inclusions with state-dependent delay
In this paper, we establish sufficient conditions for the existence of mild solutions for fractional integro-differential inclusions with state-dependent delay. The techniques rely on fractional calculus, multivalued mapping on a bounded set and Bohnenblust-Karlin's fixed point theorem. Finally, we present an example to illustrate the theory.
Fredholm alternative for nonlinear operators in Banach spaces and its applications to differential and integral equations
Fredholmness of an abstract differential equation of elliptic type.
From convergence of operator semigroups to gene expression, and back again
The subject of the paper is reciprocal influence of pure mathematics and applied sciences. We illustrate the idea by giving a review of mathematical results obtained recently, related to the model of stochastic gene expression due to Lipniacki et al. [38]. In this model, featuring mRNA and protein levels, and gene activity, the stochastic part of processes involved in gene expression is distinguished from the part that seems to be mostly deterministic, and the dynamics is expressed by means of a...
Functionals on function and sequence spaces connected with the exponential stability of evolutionary processes
The exponential stability property of an evolutionary process is characterized in terms of the existence of some functionals on certain function spaces. Thus are generalized some well-known results obtained by Datko, Rolewicz, Littman and Van Neerven.
Fundamental operator-functions of degenerate differential and difference-differential operators in Banach spaces which have a Noether operator in the principal part.
Funkcionální rovnice v nelineární analýze. Věnováno G. Prodimu, velkému učiteli a drahému příteli.
Furi–Pera fixed point theorems in Banach algebras with applications
In this work, we establish new Furi–Pera type fixed point theorems for the sum and the product of abstract nonlinear operators in Banach algebras; one of the operators is completely continuous and the other one is -Lipchitzian. The Kuratowski measure of noncompactness is used together with recent fixed point principles. Applications to solving nonlinear functional integral equations are given. Our results complement and improve recent ones in [10], [11], [17].
Fuzzy solutions for boundary value problems with integral boundary conditions.
General existence principles for nonlocal boundary value problems with -Laplacian and their applications.
General existence results for nonconvex third order differential inclusions.
General method of regularization. I: Functionals defined on BD space
The aim of this paper is to prove that the relaxation of the elastic-perfectly plastic energy (of a solid made of a Hencky material) is the lower semicontinuous regularization of the plastic energy. We find the integral representation of a non-locally coercive functional. In part II, we will show that the set of solutions of the relaxed problem is equal to the set of solutions of the relaxed problem proposed by Suquet. Moreover, we will prove the existence theorem for the limit analysis problem.
General method of regularization. II: Relaxation proposed by suquet
The aim of this paper is to prove that the relaxation of the elastic-perfectly plastic energy (of a solid made of a Hencky material) is the lower semicontinuous regularization of the plastic energy. We find the integral representation of a non-locally coercive functional. We show that the set of solutions of the relaxed problem is equal to the set of solutions of the relaxed problem proposed by Suquet. Moreover, we prove an existence theorem for the limit analysis problem.