B. S. Lalli

TL;DR: In this paper, a criterion for the existence of a positive solution for the first order difference equation Δ(n − cxn − m) + pnxn − k = 0, pn ⩾ 0 is established.

TL;DR: In this paper, sufficient conditions for the oscillation of the nonlinear second order differential equation were established, and a systematic study was attempted which extends and correlates a number of existing results. But none of the results were considered in this paper.

TL;DR: In this article, the authors obtained sufficient conditions for the oscillation of all solutions and existence of positive solutions of the neutral difference equation Δ (x n + cx n − m ) + p n x n − k = 0.

TL;DR: In this article, the authors established new oscillation criteria for second order nonlinear differential equations of the form if(a(t) ψ(x(t)) ẋ(t)),suẋ + p(t), Ẇ(t)+ q(t + f(x,t)) = 0 for all large values of t. These criteria are obtained by using integral averaging techniques.

TL;DR: In this article, the generalized Emden-Fowler equation with retarded arguments was extended and improved with fundamental oscillation criteria for superlinear, sublinear, and linear differential equations.