An Existence Result for a Nonlinear Volterra Integral Equation in a Hilbert Space

Autor:	Gustaf Gripenberg
Rok vydání:	1978
Předmět:	Kernel (set theory) Applied Mathematics Mathematical analysis Hilbert space Monotonic function Function (mathematics) Volterra integral equation Computational Mathematics symbols.namesake Nonlinear system symbols Uniqueness Special case Analysis Mathematics
Zdroj:	SIAM Journal on Mathematical Analysis. 9:793-805
ISSN:	1095-7154 0036-1410
DOI:	10.1137/0509061
Popis:	We study equations of the form \[u(t) + \int_0^t {a(t - s)gu(s)ds \ni f(t)} ,\quad t \geqq 0\] on a real Hilbert space H. The unknown function is u and a, g, f are given. It is assumed that the kernel a is operator-valued (real-valued as a special case) and g is an arbitrary maximal monotone operator in H. The method can also be applied to time-varying nonlinearity. We prove an existence and uniqueness result that extends earlier results by Londen and Barbu. Finally an application is given.
Databáze:	OpenAIRE
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