Lebesgue regularity for differential difference equations with fractional damping
Corresponding Author
Carlos Lizama
Facultad de Ciencias, Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Las Sophoras 173, Estación Central, Santiago, Chile
Correspondence
Carlos Lizama, Facultad de Ciencias, Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Las Sophoras 173, Estación Central, Santiago, Chile.
Email: [email protected]
Search for more papers by this authorMarina Murillo-Arcila
Institut de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, Campus del Riu Sec s/n, 12071, Castelló, Spain
Search for more papers by this authorClaudio Leal
Facultad de Ciencias, Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Las Sophoras 173, Estación Central, Santiago, Chile
Search for more papers by this authorCorresponding Author
Carlos Lizama
Facultad de Ciencias, Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Las Sophoras 173, Estación Central, Santiago, Chile
Correspondence
Carlos Lizama, Facultad de Ciencias, Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Las Sophoras 173, Estación Central, Santiago, Chile.
Email: [email protected]
Search for more papers by this authorMarina Murillo-Arcila
Institut de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, Campus del Riu Sec s/n, 12071, Castelló, Spain
Search for more papers by this authorClaudio Leal
Facultad de Ciencias, Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Las Sophoras 173, Estación Central, Santiago, Chile
Search for more papers by this authorAbstract
We provide necessary and sufficient conditions for the existence and uniqueness of solutions belonging to the vector-valued space of sequences
for equations that can be modeled in the form
A is a closed linear operator with domain D(A) defined on X, and G is a nonlinear function. The operator Δγ denotes the fractional difference operator of order γ>0 in the sense of Grünwald-Letnikov. Our class of models includes the discrete time Klein-Gordon, telegraph, and Basset equations, among other differential difference equations of interest. We prove a simple criterion that shows the existence of solutions assuming that f is small and that G is a nonlinear term.
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