Nonoscillation theory of nonlinear differential equations of Emden–Fowler type with variable exponents

Abstract We consider the Emden–Fowler differential equation with variable exponents and establish necessary, sufficient and both necessary and sufficient conditions for the existence of nonoscillatory solutions of this equation with three different patterns of asymptotic behavior at infinity. The Schauder–Tikhonov fixed point theorem and duality principle are used for this purpose.