We study the existence of monotone solutions approaching zero as t --> infinity of the functional differential equation (a(t)Phi(p)(x'))' = b(t)integral(x(g(t))), Phi(p)(u) = /u/(p-2)u p > 1, where a, b are positive continuous functions on [0, infinity). These criteria involve the mutual asymptotic behavior of the coefficients a, b and also give, as a simple consequence, some results about the qualitative behavior of oscillatory solutions. Relationships between the, case without deviating argument and the functional one, enlightening both similarities and substantial differences, are treated as well.
On decaying solutions for functional differential equations with p-Laplacian / M. CECCHI;Z. DOSLA; M. MARINI. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - STAMPA. - 47-7:(2001), pp. 4387-4398. [10.1016/S0362-546X(01)00553-3]
On decaying solutions for functional differential equations with p-Laplacian
MARINI, MAURO
2001
Abstract
We study the existence of monotone solutions approaching zero as t --> infinity of the functional differential equation (a(t)Phi(p)(x'))' = b(t)integral(x(g(t))), Phi(p)(u) = /u/(p-2)u p > 1, where a, b are positive continuous functions on [0, infinity). These criteria involve the mutual asymptotic behavior of the coefficients a, b and also give, as a simple consequence, some results about the qualitative behavior of oscillatory solutions. Relationships between the, case without deviating argument and the functional one, enlightening both similarities and substantial differences, are treated as well.
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