*Correspondence: [email protected] Department of Information Engineering, China University of Geosciences Great Wall College, Baoding, Hebei 071000, P.R. China Abstract In this paper, we use monotone iterative technique in the presence of (coupled) upper and lower solutions in the reversed order to discuss the existence of extremal solutions (quasi-solutions) for causal differential equations wit...

In this work we consider the existence of traveling plane wave solutions of systems of delayed lattice differential equations in competitive Lotka-Volterra type. Employing iterative method coupled with the explicit construction of upper and lower solutions in the theory of weak quasi-monotone dynamical systems, we obtain a speed, c∗, and show the existence of traveling plane wave solutions conn...

Existence of solutions of differential and integral equations is subject of numerous investigations see, e.g., the monographs 1–3 or 4 . Moreover, a lot of work in this domain is devoted to the existence of solutions in certain special classes of functions e.g., positive functions or monotone functions . We merely mention here the result obtained by Caballero et al. 5 concerning the existence o...

The ratio monotonicity of a polynomial is a stronger property than log-concavity. Let P (x) be a polynomial with nonnegative and nondecreasing coefficients. We prove the ratio monotone property of P (x+ 1), which leads to the log-concavity of P (x+ c) for any c ≥ 1 due to Llamas and Mart́ınez-Bernal. As a consequence, we obtain the ratio monotonicity of the Boros-Moll polynomials obtained by Che...

A function F defined on all subsets of a finite ground set E is quasiconcave if F (X∪Y ) ≥ min{F (X), F (Y )} for all X, Y ⊂ E. Quasi-concave functions arise in many fields of mathematics and computer science such as social choice, theory of graph, data mining, clustering and other fields. The maximization of quasi-concave function takes, in general, exponential time. However, if a quasi-concav...

We prove L1{contraction principle and uniqueness of solutions for quasilinear elliptic{parabolic equations of the form @t[b(u)] div[a(ru; b(u))] + f(b(u)) = 0 in (0; T ) ; where b is monotone nondecreasing and continuous. We only assume that u is a weak solution of nite energy (see [1]). In particular, we do not suppose that the distributional derivative @t[b(u)] is a bounded Borel measure or a...

Impulsive differential equations are a basic tool for studying evolution processes of real life phenomena that are subjected to sudden changes at certain instants. In view of multiple applications of the impulsive differential equations, it is necessary to develop the methods for their solvability. Unfortunately, a comparatively small class of impulsive differential equations can be solved anal...

Shannon OR-capacity $C_{\rm OR}(G)$ of a graph $G$, that is the traditionally more often used AND-capacity complementary graph, homomorphism monotone parameter therefore OR}(F\times G)\leqslant\min\{C_{\rm OR}(F),C_{\rm OR}(G)\}$ holds for every pair graphs, where $F\times G$ categorical product graphs $F$ and $G$. Here we initiate study question when could expect equality in this inequality. U...

This paper studies the boundedness, global asymptotic stability, and periodicity of positive solutions of the equation xn f xn−2 /g xn−1 , n ∈ N0, where f, g ∈ C 0,∞ , 0,∞ . It is shown that if f and g are nondecreasing, then for every solution of the equation the subsequences {x2n} and {x2n−1} are eventually monotone. For the case when f x α βx and g satisfies the conditions g 0 1, g is nondec...

we prove a strong convergence result for a sequence generated by halpern's type iteration for approximating a common fixed point of a countable family of quasi-lipschitzian mappings in a real hilbert space. consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...