Solvability of impulsive neutral evolution differential inclusions with state-dependent delay

Authors:
Wen-Sheng Li;Yong-Kui Chang;Juan J. Nieto
Affiliations:
Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, PR China;Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, PR China;Departamento de Analisis Matematico, Facultad de Matematicas, Universidad de Santiago de Compostela, Santiago de Compostela, 15782, Spain
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2009

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Abstract

In this paper, we prove the existence of mild solutions for a first order impulsive neutral evolution differential inclusion with state-dependent delay. We transform it into an integral equation and use a fixed point theorem for condensing multi-valued maps. As an application of the main theorem, we consider the case when the multi-valued nonlinearity has sub-linear growth in the state variable.