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Asymptotic behaviour of solutions of a differential equation with p-Laplacian and a forcing term. (English) Zbl 1165.34367

Summary: The authors consider the nonlinear second order differential equation with a forcing term

(a(t)|y ' | p-1 y ' ) ' +r(t)|v| λ sgny=e(t),

where p>0, λ>0, a(t)>0, and r(t)>0. Various asymptotic properties of solutions are studied including oscillation, convergence to a limit, boundedness, and the nonlinear limit-point/limit-circle and the strong nonlinear limit-point/limit-circle properties. Examples illustrating the results are also included.

34D05Asymptotic stability of ODE
34B20Weyl theory and its generalizations
34C11Qualitative theory of solutions of ODE: growth, boundedness
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory