Criticality of one term 2n-order self-adjoint differential equations

• Main Authors: Michal Veselý, Petr Hasil
• Format: Article
• Language: English
• Published: University of Szeged 2012-05-01
• Series: Electronic Journal of Qualitative Theory of Differential Equations
• Subjects: one term differential operator; principal system of solutions; subcritical operator; p-critical operator
• Online Access: http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=1090

We analyse the criticality (the existence of linear dependent principal solutions at $\infty$ and $-\infty$) of the one term $2n$-order differential equation $(r y^{(n)})^{(n)} = 0$. Using the structure of the principal and the non-principal system of solutions, we find the equivalent conditions of subcriticality and at least $p$-criticality of this equation.