Existence of non-oscillatory solutions for second-order advanced half-linear differential equations

Abstract

In this article, we establish the necessary and sufficient conditions for existence of non-oscillatory solutions for the second-order advanced half-linear differential equation $$ ig(r(t)|x'(t)|^{alpha-1}x'(t)ig)'+p(t)|x(h(t)ig)|^{alpha-1}x(h(t))=0, quad tgeq t_0. $$ The obtained results generalize some well-known theorems in the literature

Keywords

• Oscillation
• nonoscillation
• half-linear
• advanced differential equation