Existence of Global Solutions for a Class of Abstract Second-Order Nonlocal Cauchy Problem with Impulsive Conditions in Banach Spaces |
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| Authors: | V Vijayakumar Hernán R Henríquez |
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| Institution: | 1. Department of Mathematics, Info Institute of Engineering, Kovilpalayam, Coimbatore, Tamil Nadu, India;2. Departamento de Matemática, Universidad de Santiago de Chile, USACH, Santiago, Chile |
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| Abstract: | In this paper, we are concerned with a class of abstract second-order nonlocal Cauchy problem with impulsive conditions in Banach spaces. First, we study the existence of mild solutions for a class of second-order nonlocal Cauchy problem with impulsive conditions in Banach spaces on an interval 0,a]. Later, we study a couple of cases where we can establish the existence of global solutions for a class of abstract second-order nonlocal Cauchy problem with impulsive conditions in Banach spaces. We apply our theory to study the existence of solutions for impulsive partial differential equations. |
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| Keywords: | Abstract second-order Cauchy problem cosine function of operators evolution equations global solutions impulsive systems mild solutions nonlocal conditions |
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