Evolution equations with causal operators

Evolution Equations with Causal Operators

In this paper we present an existence result for causal functional evolution equations. The result is obtained under a condition with respect to the Hausdorff measure of noncompactness. An application with partial differential equations is given to illustrate our main result. Mathematics subject classification (2010): 34A07, 34A08.

Set Differential Equations with Causal Operators

Differential equations involving causal operators have gained much attention of late and some results are assembled in a recent monograph [1]. The term causal is adopted from the engineering literature. Basically, a causal operator is a nonanticipative operator. The theory of these operators has the powerful quality of unifying ordinary differential equations, integrodifferential equations, dif...

Differential equations involving causal operators with nonlinear periodic boundary conditions

The notion of causal operators is extended to periodic boundary value problems with nonlinear boundary conditions in this paper. By utilizing the monotone iterative technique and the method of lower and upper solutions (resp. weakly coupled lower and upper solutions), we establish the existence of the extremal solutions (resp. weakly coupled extremal quasi-solutions) for nonlinear periodic boun...

Root Operators and “Evolution” Equations

Root-operator factorization à la Dirac provides an effective tool to deal with equations, which are not of evolution type, or are ruled by fractional differential operators, thus eventually yielding evolution-like equations although for a multicomponent vector. We will review the method along with its extension to root operators of degree higher than two. Also, we will show the results obtained...

Evolution Equations Governed by Elliptic Operators