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On Impulsive Hyperbolic Differential Inclusions with Nonlocal Initial Conditions

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Abstract

This paper is focused mainly upon existence of solutions for a second-order impulsive hyperbolic differential inclusions with nonlocal initial conditions. By using some well-known fixed-point theorems, existence theorems are established when the multivalued map has convex or nonconvex values. As applications of these main theorems, some consequences are given for the sublinear growth cases.

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Correspondence to Y.-K. Chang.

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Communicated by F. Zirilli

Y.-K. Chang was supported by “Qing Lan” Talent Engineering Funds (QL-05-16A), by Lanzhou Jiaotong University, the Scientific Research Fund of Gansu Provincial Education Department (0704-14). J.J. Nieto was supported by Ministerio de Educacion y Ciencia and FEDER, Project MTM2007-61724, and by Xunta de Galicia and FEDER, Project PGIDIT05PXIC20702PN.

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Chang, YK., Nieto, J.J. & Li, WS. On Impulsive Hyperbolic Differential Inclusions with Nonlocal Initial Conditions. J Optim Theory Appl 140, 431–442 (2009). https://doi.org/10.1007/s10957-008-9468-1

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