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.
The paper presents an existence result for global solutions to the finite dimensional differential inclusion being defined on a closed set A priori bounds for such solutions are provided.
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.
This paper is concerned with the existence of mild solutions for impulsive semilinear differential equations with nonlocal conditions. Using the technique of measures of noncompactness in Banach and Fréchet spaces of piecewise continuous functions, existence results are obtained both on bounded and unbounded intervals, when the impulsive functions and the nonlocal item are not compact in the space of piecewise continuous functions but they are continuous and Lipschitzian with respect to some measure...
The aim of this paper is to give an existence theorem for a semilinear equation of evolution in the case when the generator of semigroup of operators depends on time parameter. The paper is a generalization of [2]. Basing on the notion of a measure of noncompactness in Banach space, we prove the existence of mild solutions of the equation considered. Additionally, the applicability of the results obtained to control theory is also shown. The main theorem of the paper allows to characterize the set...
In this paper we investigate the existence of mild solutions to second order initial value problems for a class of delay integrodifferential inclusions with nonlocal conditions. We rely on a fixed point theorem for condensing maps due to Martelli.