We study asymptotic properties of solutions of the nonoscillatory half-linear differential equation (a(t)Phi(x'))' + b(t)Phi(x) = 0 where the functions a, b are continuous for t >= 0, a(t) > 0 and Phi(u) = vertical bar u vertical bar(p-2)u, p > 1. In particular, the existence and uniqueness of the zero-convergent solutions and the limit characterization of principal solutions are proved when the function b changes sign. An integral characterization of the principal solutions, the boundedness of all solutions, and applications to the Riccati equation are considered as well.
Half-Linear Differential Equations with Oscillating Coefficient / M. CECCHI;Z. DOSLA; M. MARINI. - In: DIFFERENTIAL AND INTEGRAL EQUATIONS. - ISSN 0893-4983. - STAMPA. - 18:(2005), pp. 1243-1256. [10.57262/die/1356059740]
Half-Linear Differential Equations with Oscillating Coefficient
MARINI, MAURO
2005
Abstract
We study asymptotic properties of solutions of the nonoscillatory half-linear differential equation (a(t)Phi(x'))' + b(t)Phi(x) = 0 where the functions a, b are continuous for t >= 0, a(t) > 0 and Phi(u) = vertical bar u vertical bar(p-2)u, p > 1. In particular, the existence and uniqueness of the zero-convergent solutions and the limit characterization of principal solutions are proved when the function b changes sign. An integral characterization of the principal solutions, the boundedness of all solutions, and applications to the Riccati equation are considered as well.File | Dimensione | Formato | |
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