Oscillation criteria for fourth‐order differential equations with middle term

Oscillation criteria for self‐adjoint fourth‐order differential equations\documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty} $$ (r(x)y^{\prime \prime })^{\prime \prime }-(q(x)y^{\prime })^{\prime }= p(x)y $$ \end{document} were established for various conditions on the coefficients r ( x ) > 0, q ( x ) and p ( x ). However, most of these results deal with the case when lim x → ∞ ∫ x 1 q ( s )  ds < +∞. In this note we give a new oscillation criterion in the case when this condition is not fulfilled, in particular when q ( x )↗ + ∞ (even with exponential growth).