Volume 20, Issue 2

We obtain an analogue of the integral Hille–Wintner comparison theorem for the half-linear differential equations of third order. We also give an example involving a differential equation of Euler type, which gives a condition under which half-linear differential equations have weak property B .

Almost paracontact metric manifolds are the famous examples of almost para-CR manifolds. We find necessary and sufficient conditions for such manifolds to be para-CR. Next we examine these conditions in certain subclasses of almost paracontact metric manifolds. Especially, it is shown that normal almost paracontact metric manifolds are para-CR. We establish necessary and sufficient conditions for paracontact metric manifolds as well as for almost para-cosymplectic manifolds to be para-CR. We find also basic curvature identities for para-CR paracontact metric manifolds and study their consequences. Among others, we prove that any para-CR paracontact metric manifold of constant sectional curvature and of dimension greater than 3 must be para-Sasakian and its curvature equal to -1. The last assertion does not hold in dimension 3. We show that a conformally flat para-Sasakian manifold is of constant sectional curvature equal to -1. New classes of examples of para-CR manifolds are established.

In this paper we study the growth and L δ -approximation, 1 ≤ δ ≤ ∞, of solutions (not necessarily entire) of Helmholtz-type equations. Moreover, we obtain the characterization of order and type of H ∈ H R , 0 < R < ∞, in terms of decay of approximation errors E n ( H , R 0 ) and En,δi(H,R0)$E^{i}_{n,\delta } (H,R_0)$, i = 1,2. Our results extend and improve the results obtained by McCoy [J. Approx. Theory 25 (1979), 153–168].

The aim of this paper is to characterize the products of Świątkowski and quasi-continuous functions.

We introduce q -nonuniform difference systems and propose q -nonuniform versions of some basic results of complete controllability and observability of linear systems such as criterions of controllability and observability, the q -duality theorem. An optimality necessary condition is also given for the case of the Ramsey model of economic growth.

In this paper we are interested in the existence and uniqueness of solutions for the Dirichlet problem associated to the degenerate nonlinear elliptic equations -∑j=1nDj[v2(x)𝒜j(x,u,∇u)]+∑j=1nbj(x)v1(x)Dju(x)+αg(x)v3(x)u(x)=f0(x)-∑j=1nDjfj(x)$-\sum _{j=1}^n D_j[v_2(x) {\cal A}_j(x, u, {\nabla }u)] + \sum _{j=1}^nb_j(x) v_1(x) D_ju(x) + {\alpha } g(x) v_3(x) u(x) = f_0(x) - \sum _{j=1}^nD_jf_j(x)$ on Ω in the setting of the weighted Sobolev spaces W01,2(Ω,v1,v2)${{W}_0^{1,2}(\Omega , v_1 , v_2)}$.

In the present paper, we examine duality results for Wolfe-type second-order fractional symmetric dual programs. These duality results are then used to investigate minimax mixed integer symmetric dual fractional programs. We also discuss self-duality results at the end.

In the present paper we investigate the existence and uniqueness of solutions of nonlinear mixed fractional integrodifferential equations with nonlocal condition in Banach spaces. The technique used in our analysis is based on fixed point theorems and Pachpatte's integral inequality.