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The Picard-Lindelöf Theorem and continuation of solutions for measure differential equations

Gastón Beltritti, Stefania Demaria, Graciela Giubergia, Fernando Mazzone (2025)

Czechoslovak Mathematical Journal

We obtain, by means of Banach's Fixed Point Theorem, convergence for the Picard iterations associated to a general nonlinear system of measure differential equations. We study the existence of left-continuous solutions defined on maximal intervals and we establish some properties of these maximal solutions.

Upper and lower solutions method for partial Hadamard fractional integral equations and inclusions

Saïd Abbas, Eman Alaidarous, Wafaa Albarakati, Mouffak Benchohra (2015)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we use the upper and lower solutions method combined with Schauder's fixed point theorem and a fixed point theorem for condensing multivalued maps due to Martelli to investigate the existence of solutions for some classes of partial Hadamard fractional integral equations and inclusions.

Well posedness and control of semilinear wave equations with iterated logarithms

Piermarco Cannarsa, Vilmos Komornik, Paola Loreti (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Motivated by a classical work of Erdős we give rather precise necessary and sufficient growth conditions on the nonlinearity in a semilinear wave equation in order to have global existence for all initial data. Then we improve some former exact controllability theorems of Imanuvilov and Zuazua.

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