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Topological Methods in Nonlinear Analysis

Existence results for evolution equations with superlinear growth
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Existence results for evolution equations with superlinear growth

Authors

  • Irene Benedetti https://orcid.org/0000-0003-0229-2206
  • Eugénio M. Rocha https://orcid.org/0000-0003-3628-6795

Keywords

Semilinear differential equation, approximation solvability method, Leray-Schauder continuation principle, Nemytskii operator

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 Caratheodory 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.

References

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I. Benedetti, L. Malaguti and V. Taddei, Nonlocal solutions of parabolic equations with strongly elliptic differential operators, J. Math. Anal. Appl. 473 (2019), 421–443.

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Published

2019-12-25

How to Cite

1.
BENEDETTI, Irene and ROCHA, Eugénio M. Existence results for evolution equations with superlinear growth. Topological Methods in Nonlinear Analysis. Online. 25 December 2019. Vol. 54, no. 2B, pp. 917 - 936. [Accessed 5 July 2025].
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Vol 54, No 2B (December 2019)

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