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2019 Existence results for evolution equations with superlinear growth
Irene Benedetti, Eugenio M. Rocha
Topol. Methods Nonlinear Anal. 54(2B): 917-936 (2019). DOI: 10.12775/TMNA.2019.101

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 $C_0$-semigroup of contractions, and a Carathéodory nonlinearity $f\colon [0,T] \times E \to F$, with $E$ and $F$ two real Banach spaces such that $E \subseteq F$, besides imposing other conditions. The case $E\neq F$ allows to treat, as an application, parabolic equations with continuous superlinear nonlinearities which satisfy a sign condition.

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Irene Benedetti. Eugenio M. Rocha. "Existence results for evolution equations with superlinear growth." Topol. Methods Nonlinear Anal. 54 (2B) 917 - 936, 2019. https://doi.org/10.12775/TMNA.2019.101

Information

Published: 2019
First available in Project Euclid: 29 December 2019

MathSciNet: MR4077470
Digital Object Identifier: 10.12775/TMNA.2019.101

Rights: Copyright © 2019 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.54 • No. 2B • 2019
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