Regularity properties of mild solutions for a class of Volterra equation with critical nonlinearities

Abadías Ullod, Luciano (Universidad de Zaragoza) ; Álvarez, Edgardo ; Lizama, Carlos

Resumen: 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.

Idioma: Inglés

DOI: 10.1216/JIE-2018-30-2-219

Año: 2018

Publicado en: JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS 30, 2 (2018), 219-256
ISSN: 0897-3962

Factor impacto JCR: 0.974 (2018)

Categ. JCR: MATHEMATICS rank: 98 / 313 = 0.313 (2018) - Q2 - T1
Categ. JCR: MATHEMATICS, APPLIED rank: 149 / 254 = 0.587 (2018) - Q3 - T2

Factor impacto SCIMAGO: 0.384 - Numerical Analysis (Q3) - Applied Mathematics (Q3)

Tipo y forma: Article (Published version)

Área (Departamento): Área Análisis Matemático (Dpto. Matemáticas)