On the integro‐differential equations with reflection
Copyright policy )On the integro‐differential equations with reflection
In this paper, by developing important properties on the composition of functions with reflection, using some exponential dichotomy properties and an application of the fixed‐point theorem, several new sufficient conditions for the existence and the uniqueness of an pseudo almost automorphic solutions with measure for some general‐type reflection integro‐differential equations. We suppose that the nonlinear part is measure pseudo almost automorphic and in which we distinguish the two constant and variable cases for the Lipschitz coefficients of the functions associated with this part. It is assumed that the linear part of the equation considered admits an exponential dichotomy. Finally, an application is given on the very interesting model of Markus and Yamabe.
- Faculté des Lettres et des Sciences Humaines de Sfax Tunisia
- Cadi Ayyad University Morocco
- University of Sfax Tunisia
- University of Kairouan Tunisia
integro-differential equations, Theory and Applications of Fractional Differential Equations, Mathematical analysis, Quantum mechanics, Converse theorem, Database, Integro-ordinary differential equations, Engineering, Differential equation, Numerical Methods for Singularly Perturbed Problems, FOS: Mathematics, Variable (mathematics), Functional Differential Equations, Numerical Analysis, One-parameter semigroups and linear evolution equations, Reflection (computer programming), Applied Mathematics, Physics, Stability theory for integral equations, Exponential function, Pure mathematics, Measure (data warehouse), Automorphic form, Lipschitz continuity, Computer science, Programming language, exponential dichotomy, Semilinear Differential Equations, Exponential dichotomy, pseudo-almost automorphic, Control and Systems Engineering, Physical Sciences, Analysis and Control of Distributed Parameter Systems, Nonlinear system, Uniqueness, Mathematics, reflection
integro-differential equations, Theory and Applications of Fractional Differential Equations, Mathematical analysis, Quantum mechanics, Converse theorem, Database, Integro-ordinary differential equations, Engineering, Differential equation, Numerical Methods for Singularly Perturbed Problems, FOS: Mathematics, Variable (mathematics), Functional Differential Equations, Numerical Analysis, One-parameter semigroups and linear evolution equations, Reflection (computer programming), Applied Mathematics, Physics, Stability theory for integral equations, Exponential function, Pure mathematics, Measure (data warehouse), Automorphic form, Lipschitz continuity, Computer science, Programming language, exponential dichotomy, Semilinear Differential Equations, Exponential dichotomy, pseudo-almost automorphic, Control and Systems Engineering, Physical Sciences, Analysis and Control of Distributed Parameter Systems, Nonlinear system, Uniqueness, Mathematics, reflection
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