78153 20220208112844.0 doi 10.1216/JIE-2018-30-2-219 sideral 97954 ART-2018-97954 eng Abadías Ullod, Luciano Universidad de Zaragoza (orcid)0000-0003-2453-7841 Regularity properties of mild solutions for a class of Volterra equation with critical nonlinearities 2018 Access copy available to the general public Unrestricted We study a class of abstract nonlinear integral equations of convolution type defined on a Banach space. We prove the existence of a unique, locally mild solution and an extension property when the nonlinear term satisfies a local Lipschitz condition. Moreover, we guarantee the existence of the global mild solution and blow up profiles for a large class of kernels and nonlinearities. If the nonlinearity has critical growth, we prove the existence of the local ¿-mild solution. Our results improve and extend recent results for special classes of kernels corresponding to nonlocal in time equations. We give an example to illustrate the application of the theorems so obtained. info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 0.974 2018 MATHEMATICS 98 / 313 = 0.313 2018 Q2 T1 MATHEMATICS, APPLIED 149 / 254 = 0.587 2018 Q3 T2 0.384 2018 Numerical Analysis 2018 Q3 Applied Mathematics 2018 Q3 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Álvarez, Edgardo Lizama, Carlos 2006 015 Universidad de Zaragoza Dpto. Matemáticas Área Análisis Matemático 30, 2 (2018), 219-256 J. integral equ. appl. JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS 0897-3962 205641 http://zaguan.unizar.es/record/78153/files/texto_completo.pdf Versión publicada 46429 http://zaguan.unizar.es/record/78153/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:78153 articulos driver 2022-02-08-11:23:25 ARTICLE