In the 1990s, after a series of experiments, behavioral psychologist and economist Daniel Kahneman his colleagues formulated following Peak-End evaluation rule: "The remembered utility pleasant or unpleasant episodes is accurately predicted by averaging Peak (most intense value) instant (or disutility) recorded during an episode near end experience", (D. et al., 1997, QJE, p. 381). Hence, simpl...

Stability in terms of two measures for nonlinear differential equations with “maxima” is studied. A special type of stability in terms of two measures is defined. The new type of stability generalizes some of the known in the literature. Sufficient conditions for the defined stability are obtained. Cone-valued continuous Lyapunov functions are applied. Method of Razumikhin as well as comparison...

in this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the lipschitz type condition. moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

We consider scalar delay differential equations x′(t) = −δx(t)+f(t, xt) (∗) with nonlinear f satisfying a sort of negative feedback condition combined with a boundedness condition. The well-known Mackey–Glass-type equations, equations satisfying the Yorke condition, and equations with maxima all fall within our considerations. Here, we establish a criterion for the global asymptotical stability...

This paper is related to the existence and approximation of solutions for impulsive functional differential equations with periodic boundary conditions. We study the existence and approximation of extremal solutions to different types of functional differential equations with impulses at fixed times, by the use of the monotone method. Some of the options included in this formulation are differe...

*Correspondence: [email protected] Department of Mathematics, Sichuan University for Nationalities, Kangding, Sichuan 626001, P.R. China Abstract In this paper, we consider a general form of nonlinear integral inequalities with the unknown function composed with a given function on the left hand side, more than one distinct nonlinear integrals on its right-hand side, and weakly singular kernels,...