EXISTENCE AND ASYMPTOTIC BEHAVIOR OF POSITIVE SOLUTIONS OF FOURTH ORDER QUASILINEAR DIFFERENTIAL EQUATIONS
EXISTENCE AND ASYMPTOTIC BEHAVIOR OF POSITIVE SOLUTIONS OF FOURTH ORDER QUASILINEAR DIFFERENTIAL EQUATIONS
The feature of the present work is to demonstrate that the method of regular variation can be effectively applied to fourth order quasilinear differential equations of the forms \begin{equation*} (|x''|^{\alpha-1}x'')'' + q(t)|x|^{\beta-1}x = 0, \end{equation*} under the assumptions that $\alpha \gt \beta$ and $q(t): [a,\infty) \to (0,\infty)$ is regularly varying …