A matrix in -algebra (fuzzy matrix) is called weakly robust if is an eigenvector of only if is an eigenvector of . The weak robustness of fuzzy matrices are studied and its properties are proved. A characterization of the weak robustness of fuzzy matrices is presented and an algorithm for checking the weak robustness is described.
When mathematical models describing various processes are analysed, the fact of existence of a positive solution is often among the basic features. In this paper, a general delayed discrete equation is considered. Sufficient conditions concerning are formulated in order to guarantee the existence of a positive solution for . An upper estimate for it is given as well. The appearance of the positive solution takes its origin in the nature of the equation considered since the results hold only...
We prove some new Opial type inequalities on time scales and employ them to prove several results related to the spacing between consecutive zeros of a solution or between a zero of a solution and a zero of its derivative for second order dynamic equations on time scales. We also apply these inequalities to obtain a lower bound for the smallest eigenvalue of a Sturm-Liouville eigenvalue problem on time scales. The results contain as special cases some results obtained for second order differential...
Some new oscillation and nonoscillation criteria for the second order neutral delay difference equation where , are positive integers and is a ratio of odd positive integers are established, under the condition
2000 Mathematics Subject Classification: 39A10.The oscillatory and nonoscillatory behaviour of solutions of the second order quasi linear neutral delay difference equation Δ(an | Δ(xn+pnxn-τ)|α-1 Δ(xn+pnxn-τ) + qnf(xn-σ)g(Δxn) = 0 where n ∈ N(n0), α > 0, τ, σ are fixed non negative integers, {an}, {pn}, {qn} are real sequences and f and g real valued continuous functions are studied. Our results generalize and improve some known results of neutral delay difference equations.
Necessary and sufficient conditions are obtained for every solution of to oscillate or tend to zero as , where , and are sequences of real numbers such that . Different ranges for are considered.