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May  2009, 8(3): 955-976. doi: 10.3934/cpaa.2009.8.955

Generalized solutions for the abstract singular Cauchy problem

Hernan R. Henriquez 1,

1. 

Departamento de Matemática, Universidad de Santiago, USACH, Casilla 307, Correo-2, Santiago, Chile

Received  March 2008 Revised  August 2008 Published  February 2009

In this work we study existence of solutions in convoluted sense for the abstract singular Cauchy problem. We relate the existence of convoluted solutions with the existence of a generalized singular evolution operator, and we establish a Hille-Yosida type theorem to characterize the existence of a local generalized singular evolution operator.
Keywords: Laplace transform., Abstract singular Cauchy problem, generalized singular evolution operator.
Mathematics Subject Classification: Primary: 34G10, 35K65; Secondary: 47D6.
Citation: Hernan R. Henriquez. Generalized solutions for the abstract singular Cauchy problem. Communications on Pure and Applied Analysis, 2009, 8 (3) : 955-976. doi: 10.3934/cpaa.2009.8.955
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