## On oscillation criteria for self-adjoint linear differential equation of the fourth order.(English)Zbl 0719.34055

The authors study the selfadjoint differential equation $$(1)\quad (r(x)y'')''+q(x)y=0,$$ where $$p(x)\in C^ 2(I)$$, q(x)$$\in C(I)$$, $$p(x)>0$$, $$x\in I=(a,b)$$, $$-\infty \leq a<b\leq \infty$$. They prove new sufficient conditions under which the equation (1) is oscillatory at b. These conditions do not require sign restrictions on the function q(x).

### MSC:

 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34A30 Linear ordinary differential equations and systems

### Keywords:

selfadjoint differential equation; oscillatory