Nonoscillation criteria and energy functional for even-order half-linear two-term differential equations

Abstract

We investigate oscillatory properties of even-order half-linear differential equations and conditions for negativity of the associated energy functional. First, using the relationship between positivity of the functional and nonoscillation of the investigated equation, we prove Hille-Nehari type nonoscillation criteria which extend criteria known in the linear case. In the second part of the paper, we present conditions which guarantee that the energy functional attains a negative value, i.e., it is unbounded below.

Keywords

• Even-order half-linear differential equation
• energy functional
• nonoscillation, Wirtinger inequality