By combining an approximation technique with the Leray-Schauder continuation principle, we prove global existence results for semilinear differential equations involving a dissipative linear operator, generating an extendable compact C0-semigroup of contractions, and a Caratheodory nonlinearity f : [0; T] x E --> F, with E and F two real Banach spaces such that E F, besides imposing other conditions. The fact that E and F can be two different spaces allows to treat, as an application, parabolic equations with continuous superlinear nonlinearities which satisfy a sign condition.
Existence results for evolution equations with superlinear growth
Benedetti, Irene
;
2019
Abstract
By combining an approximation technique with the Leray-Schauder continuation principle, we prove global existence results for semilinear differential equations involving a dissipative linear operator, generating an extendable compact C0-semigroup of contractions, and a Caratheodory nonlinearity f : [0; T] x E --> F, with E and F two real Banach spaces such that E F, besides imposing other conditions. The fact that E and F can be two different spaces allows to treat, as an application, parabolic equations with continuous superlinear nonlinearities which satisfy a sign condition.File in questo prodotto:
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