The (almost) 1-cover lifting property of omega-limit sets is established for nonmonotone skew-product semiflows, which are comparable to uniformly stable eventually strongly monotone skew-product semiflows. These results are then applied to study the asymptotic behavior of solutions to the nonmonotone comparable systems of ODEs, reaction-diffusion systems, differential systems with time delays ...

The purpose of this paper is to prove some coupled fixed point theorems for mapping having the mixed monotone property in partially ordered metric sapces which are generalization of the main results of Bhaskar and Lakshmikantham [T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal.TMA 65(2006) 1379 1393]. We support our resul...

Using the coupling method and Girsanov’s theorem, we study the strong Feller property and irreducibility for the transition probabilities of stochastic differential equations with non-Lipschitz and monotone coefficients. Then, the exponential ergodicity and the spectral gap for the corresponding transition semigroups are obtained under fewer assumptions.

The theory of differential inclusions provides certain sufficient conditons for the uniqueness of Filippov solutions such as one-sided Lipschitzian property or maximal monotone condition. When applied to piecewise affine dynamical systems, these conditions impose rather strong conditions. In this paper, we provide less restrictive conditions for uniqueness of Filippov solutions for the bimodal ...

In the context of decision under uncertainty, we characterize the 2-additive Choquet integral on the set of fictitious acts called binary alternatives or binary actions. This characterization is based on a fundamental property called MOPI which permits us to relate belief functions and the 2additive Choquet integral. Keywords—Capacity, Möbius transform, Choquet integral, k-monotone function, Be...

Hyperbolic conservation laws (HCLs) are a class of partial differential equations that model transport processes. Many important phenomena in natural sciences are described by them. In this paper we consider finite difference methods for the approximation of HCLs. As HCLs describe an evolution in time, one may distinguish explicit and implicit schemes by the corresponding time integration mecha...

A hereditary property of graphs is a collection of (isomorphism classes of) graphs which is closed under taking induced graphs, and contains arbitrarily large structures. Given a family F of graphs, the family P(F) of graphs containing no member of F as an induced subgraph is a hereditary property, and every hereditary property of graphs arises in this way. A hereditary property of other combin...

In this article we present a variant of the basic result of "T. Gnana. Bhaskar and V. Lakshmikanthan, Fixed point theorem in partially ordered metric spaces and applications, Nonlinear Anal. TMA, 65 (2006), 1379–1393." to …nd the coupled …xed points of multivalued mappings without mixed monotone property in cone metric space involving non-normal cones. As applications we prove the existence of ...

In 1974, Sugeno introduced the notion of fuzzy measure and integral to evaluate nonadditive or non-linear quality in systems engineering. In the same year, Dobrakov independently introduced the notion of submeasure from mathematical point of view to show that most of the theory of countably additive measures remain valid for such measures. Fuzzy measures and submeasures are both special kinds o...

We extend the Malitsky-Tam forward-reflected-backward (FRB) splitting method for inclusion problems of monotone operators to nonconvex minimization problems. By assuming generalized concave Kurdyka-Łojasiewicz (KL) property a quadratic regularization objective, we show that FRB converges globally stationary point objective and enjoys finite length property. Convergence rates are also given. The...