Existence of solution for non-autonomous semilinear measure driven equations

Summary: This work is concerned with the existence of a solution for non-autonomous measure driven semilinear equation in Banach spaces. The Schauder fixed point theorem is utilized to explore the existence of a solution. Finally, we construct an example to demonstrate the acquired outcomes.

[1]  Jitao Sun,et al.  Practical stability of nonlinear measure differential equations , 2018, Nonlinear Analysis: Hybrid Systems.

[2]  Jitao Sun,et al.  Approximate controllability of semilinear measure driven systems , 2018, Mathematische Nachrichten.

[3]  B. Satco,et al.  On Regulated Functions , 2018, Fasciculi Mathematici.

[4]  Madhukant Sharma,et al.  Approximate controllability of a non-autonomous differential equation , 2018, Proceedings - Mathematical Sciences.

[5]  Ignacio Márquez Albés,et al.  Extremal solutions of systems of measure differential equations and applications in the study of Stieltjes differential problems , 2018, 1803.08860.

[6]  Jitao Sun,et al.  Controllability of measure driven evolution systems with nonlocal conditions , 2017, Appl. Math. Comput..

[7]  Antonín Slavík,et al.  Extremal solutions of measure differential equations , 2016 .

[8]  Jitao Sun,et al.  Measures of noncompactness in spaces of regulated functions with application to semilinear measure driven equations , 2016 .

[9]  Jitao Sun,et al.  Existence of solutions for semilinear measure driven equations , 2015 .

[10]  B. Satco.  Regulated solutions for nonlinear measure driven equations , 2014 .

[11]  B. Satco,et al.  Measure differential inclusions - between continuous and discrete , 2014 .

[12]  Remco I. Leine,et al.  Global uniform symptotic attractive stability of the non-autonomous bouncing ball system , 2012 .

[13]  S. G. Pandit,et al.  Stability and asymptotic equivalence of measure differential equations , 1979 .

[14]  S. Leela,et al.  Stability of measure differential equations. , 1974 .

[15]  R. R. Sharma.  An abstract measure differential equation , 1972 .

[16]  J. Mesquita.  Measure functional differential equations and impulsive functional dynamic equations on time scales , 2012 .

[17]  C. S. Hönig.  Volterra Stieltjes-Integral Equations , 1975 .

[18]  P. C. Das,et al.  Existence and stability of measure differential equations , 1972 .