Limit Circle/Limit Point Criteria for Second-Order Sublinear Differential Equations with Damping Term

Limit Circle/Limit Point Criteria for Second-Order Sublinear Differential Equations with Damping Term

and Applied Analysis 3 2. Main Results To simplify notations, let α 1/2 k 1 and β 2k 1 /2 k 1 . We define

Limit Circle/Limit Point Criteria for Second-Order Superlinear Differential Equations with a Damping Term

Oscillation Criteria for Second-order Nonlinear Differential Equations with Damping Term

By employing a generalized Riccati technique and an integral averaging technique, new oscillation criteria are established for a class of second-order nonlinear differential equations with damping term. These criteria extend, improve and unify a number of existing results and handle the cases which are not covered by the known criteria. In particular, several interesting examples that illustrat...

Oscillation Criteria for a Class of Second-Order Nonlinear Differential Equations with Damping Term

and Applied Analysis 3 Proof. Assume that 1.1 has a nonoscillatory solution x t . Without loss of generality, suppose that it is an eventually positive solution if it is an eventually negative solution, the proof is similar , that is, x t > 0 for all t ≥ t0. We consider the following three cases. Case 1. Suppose that x′ t is oscillatory. Then there exists t1 ≥ t0 such that x′ t1 0. From 1.1 , w...

Oscillation Criteria for Second Order Half-linear Differential Equations with Damping Term

By using averaging functions, several new oscillation criteria are established for the half-linear damped differential equation-2-2-2-2 r(t) (x) +p(t) |x| x,r(t) (x) +q(t)|x| x=0, dx dx dx dx dt dt dt dt α α α α ψ ϕ ψ ⎛ ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ and the more general equation-2-2 r(t) (x) +p(t) g(x),r(t) (x) +q(t)g(x)=0, d dx dx dx dx dt dt dt dt dt α α ψ ϕ ψ ⎛ ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ...