Oscillation properties of two term linear differential equations

Abstract

The two term differential equations L n [ y ] + p y = 0 {L_n}[y] + py = 0 , where L 0 [ y ] = y , L i [ y ] = ( ρ i ( t ) L i [ y ( t ) ] ) ′ {L_0}[y] = y,{L_i}[y] = ({\rho _i}(t){L_i}[y(t)])’ , were recently studied by Z. Nehari. In this paper we give integral conditions which assure the integrability of ρ 1 − 1 ( t ) p ( t ) \rho _1^{ - 1}(t)p(t) on [ a , ∞ ) [a,\infty ) when L n [ y ] {L_n}[y] is disconjugate. By changing the integral conditions slightly we then prove that the equation has n linearly independent oscillatory solutions.