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In this paper we obtain some new oscillation criteria for the second order nonlinear neutral delay dynamic equation (𝑥(𝑡) – 𝑝(𝑡)𝑥(𝑡 – । 1 )) ΔΔ + 𝑞(𝑡)𝑓(𝑥(𝑡 – । 2 )) = 0, on a time scale 𝕋. Moreover, a new sufficient condition for the oscillation sublinear equation (𝑥(𝑡) – 𝑝(𝑡)𝑥(𝑡 – । 1 )) ″ +...
For some class of nonuniformly degenerated elliptic equations of second order, a necessary and sufficient condition for boundary points to be regular is found. This condition is an analogue of Wiener's criterion for the Laplace equation.
The goal of this paper is to present some extensions of the method of quasi-reversibility applied to an ill-posed Cauchy problem associated with an unbounded linear operator in a Hilbert space. The key point to our proof is the use of a new perturbation to construct a family of regularizing...
We study the pointwise convergence of Walsh–Fourier series on the class of functions of generalized 𝑝-bounded fluctuation.
We estimate the rate of convergence of the Bézier variant of Durrmeyer type Meyer–König and Zeller operators for functions with derivatives of bounded variation defined on 0, 1.
This paper contains some results connected with topologies generated by lower and semi-lower density operators. We show that in some measurable spaces (𝑋, 𝑆, 𝐽) there exists a semi-lower density operator which does not generate a topology. We investigate some properties of nowhere dense sets,...
The strong asymptotics of monic extremal polynomials with respect to the norm 𝐿𝑝( σ ) are studied. The measure σ is concentrated on the segment –1, 1 plus a finite set of mass points in a region of the complex plane exterior to the segment –1, 1.
We consider finite systems of straight lines in the Euclidean plane 𝐑 2 with some of their combinatorial characteristics. Euler's formula is applied for obtaining results of combinatorial type for such systems. In particular, a lower estimate for the number of two-sided and three-sided domains...
Let 𝑋 be a completely regular Hausdorff space, 𝐸 a quasi-complete locally convex space, 𝐶(𝑋) (resp. 𝐶 𝑏 (𝑋)) the space of all (resp. all, bounded), scalar-valued continuous functions on 𝑋, and 𝐵(𝑋) and 𝐵 0 (𝑋) be the classes of Borel and Baire subsets of 𝑋. We study the spaces 𝑀 𝑡 (𝑋,𝐸), 𝑀 τ...
Some “sharp” conditions are established for a kind of linear neutral difference equations with continuous arguments not to possess eventually positive solutions. The existence and asymptotic behavior are obtained for positive solutions of the kind of equations. The results for linear cases are...
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