β Scribed by Xiaojing Yang
No coin nor oath required. For personal study only.
In this paper, we consider the unboundedness of solutions of the following differential equation
(Ο~p~(xβ²))β² + (p β 1)[Ξ±____Ο~p~(x^+^) β Ξ²Ο~p~(x^β^)] = f(x)xβ² + g(x) + h(x) + e(t)
where Ο~p~(u) = |u|^pβ 2^ u, p > 1, x^Β±^ = max {Β±x, 0}, Ξ± and Ξ² are positive constants satisfying $\alpha ^{-{{1} \over {p}}} + \beta ^{-{{1} \over {p}}} = {{2m} \over {n}}$ with m, n β N and (m, n) = 1, f and g are continuous and bounded functions such that lim~xβΒ±β~g(x) β g(Β±β) exists and h has a sublinear primitive, e(t) is 2Ο~p~βperiodic and continuous. (Β© 2004 WILEYβVCH Verlag GmbH & Co. KGaA, Weinheim)
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