Existence results for evolution equations with superlinear growth - Benedetti, Irene; Rocha, Eugénio M. (Topological Methods in Nonlinear Analysis, 2019)
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 C_0-semigroup of contractions, and a Caratheodory nonlinearity f[0,T] × E → F, with E and F two real Banach spaces such that E F, besides imposing other conditions. The case E eq F allows to treat, as an application, parabolic equations with continuous superlinear nonlinearities which satisfy a sign condition.