In the paper we prove a variant of the well known Filippov-Pliss lemma for evolution inclusions given by multivalued perturbations of m-dissipative differential equations in Banach spaces with uniformly convex dual. The perturbations are assumed to be almost upper hemicontinuous with convex weakly compact values and to satisfy one-sided Peron condition. The result is then applied to prove the connectedness of the solution set of evolution inclusions without compactness and afterward the existence of attractor of autonomous evolution inclusion when the perturbations are one-sided Lipschitz with negative constant.
The reliable solution of nonlinear parameter estimation problems is an important computation problem in chemical engineering. The present paper is devoted to an application of a nonlinear solving process to a system of transcendent equations. In such systems we may define the values of the parameters Λ 12 and Λ 21 to the Wilson equation on the base of the activity coefficients at infinite dilution. The Wilson equation was used in the mathematical model for prediction of mixture flash point temperature.
In this paper we prove that almost all, in Baire sense, differential equations with Scorza Dragoni right-hand side, defined on closed convex cone of a Banach space, have unique solution. This solution depends continuously on the right-hand side and on the initial condition. The results are applied to fuzzy differential equations and to differential inclusions.
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