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Existence of extremal periodic solutions for nonlinear evolution inclusions

Nikolaos S. Papageorgiou, Nikolaos Yannakakis (2001)

Archivum Mathematicum

We consider a nonlinear evolution inclusion defined in the abstract framework of an evolution triple of spaces and we look for extremal periodic solutions. The nonlinear operator is only pseudomonotone coercive. Our approach is based on techniques of multivalued analysis and on the theory of operators of monotone-type. An example of a parabolic distributed parameter system is also presented.

Existence of mild solutions for fractional evolution equations with nonlocal initial conditions

Pengyu Chen, Yongxiang Li, Qiang Li (2014)

Annales Polonici Mathematici

This paper discusses the existence of mild solutions for a class of semilinear fractional evolution equations with nonlocal initial conditions in an arbitrary Banach space. We assume that the linear part generates an equicontinuous semigroup, and the nonlinear part satisfies noncompactness measure conditions and appropriate growth conditions. An example to illustrate the applications of the abstract result is also given.

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