MOTIVATED by various significant applications to non-Newtonian fluid theory, diffusion offlows in porous media, nonlinear elasticity, and theory of capillary surfaces, several authors(see refs.[1,2] and references cit...MOTIVATED by various significant applications to non-Newtonian fluid theory, diffusion offlows in porous media, nonlinear elasticity, and theory of capillary surfaces, several authors(see refs.[1,2] and references cited therein ) have recently studied the existence of periodicsolutions and other properties for the following differential equation:展开更多
The boundedness of all solutions is shown for Duffing-type equations $\frac{{d^2 x}}{{dt^2 }} + x^{2n + 1} + \sum\limits_{j = 0}^{2n} {x^j p_j (t) = 0, n \geqslant 1,} $ wherep 1,p 2,...,p 2n are of period 1 and of Li...The boundedness of all solutions is shown for Duffing-type equations $\frac{{d^2 x}}{{dt^2 }} + x^{2n + 1} + \sum\limits_{j = 0}^{2n} {x^j p_j (t) = 0, n \geqslant 1,} $ wherep 1,p 2,...,p 2n are of period 1 and of Lipschitzian continuity andp n+1,...,p 2n are of Zygmundian continuity. This conclusion implies that the boundedness phenomenon for the Duffing-type equations does not require the smoothness in the time-variable, thus answering the question posed by Dieckerhoff and Zehnder.展开更多
文摘MOTIVATED by various significant applications to non-Newtonian fluid theory, diffusion offlows in porous media, nonlinear elasticity, and theory of capillary surfaces, several authors(see refs.[1,2] and references cited therein ) have recently studied the existence of periodicsolutions and other properties for the following differential equation:
文摘The boundedness of all solutions is shown for Duffing-type equations $\frac{{d^2 x}}{{dt^2 }} + x^{2n + 1} + \sum\limits_{j = 0}^{2n} {x^j p_j (t) = 0, n \geqslant 1,} $ wherep 1,p 2,...,p 2n are of period 1 and of Lipschitzian continuity andp n+1,...,p 2n are of Zygmundian continuity. This conclusion implies that the boundedness phenomenon for the Duffing-type equations does not require the smoothness in the time-variable, thus answering the question posed by Dieckerhoff and Zehnder.
