Oscillation in second order functional equations with deviating arguments

Bhagat Singh

doi:10.1155/s0161171281000094

Abstract

For the pair of functional equations urn:x-wiley:01611712:media:ijmm174267:ijmm174267-math-0001 and urn:x-wiley:01611712:media:ijmm174267:ijmm174267-math-0002 sufficient conditions have been found to cause all solutions of equation (A) to be oscillatory. These conditions depend upon a positive solution of equation (B).

Highlights

(r(t)y’(t))’ p(t)h(y(g(t))) 0 sufficient conditions have been found to cause all solutions of equation (A) to be oscillatory
The failure in study of equation (i.i) leads us to this work in which we present a different approach to study the oscillation of equation (i.I) which may be sublinear, superlinear, retarded or advanced
Graef and Spikes [i], Hammett [2], Kusano and Onose [5,6], Philos and Starkos [7], this author [i0,ii] have studied asymptotic nonoscillation with regard to equation (i.i)

Summary

Introduction

For the pair of functional equations (A) (r(t)y’(t))’ p(t)h(y(g(t))) 0 sufficient conditions have been found to cause all solutions of equation (A) to be oscillatory. These conditions depend upon a positive solution of equation (B). In this work, is to seek the oscillatory behavior of the equation Rankin [8] presented a new approach to study the oscillatory behavior of the ordinary differential equation y’’(t) + p(t)y(t) f(t), (1.5)

Results

Conclusion