In this article, we investigate the existence of positive solutions of a singular quasilinear elliptic system for which the cooperative structure is not required. The approach is based on the Schauder fixed point theo...In this article, we investigate the existence of positive solutions of a singular quasilinear elliptic system for which the cooperative structure is not required. The approach is based on the Schauder fixed point theorem combined with perturbation arguments that involve the singular terms.展开更多
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
We prove the boundedness of all solutions for the equation x＂ ＋ V＇（x） = DxG（x,t）, where V（x） is of singular potential, i.e., limx→-1 Y（x） = ∞, and G（x, t） is bounded and periodic in t. We give sufficien...We prove the boundedness of all solutions for the equation x＂ ＋ V＇（x） = DxG（x,t）, where V（x） is of singular potential, i.e., limx→-1 Y（x） = ∞, and G（x, t） is bounded and periodic in t. We give sufficient conditions on V（x） and G（x, t） to ensure that all solutions are bounded.展开更多
基金supported by the Europeanprogram Averroes-Erasmus Mundus(1872)
文摘In this article, we investigate the existence of positive solutions of a singular quasilinear elliptic system for which the cooperative structure is not required. The approach is based on the Schauder fixed point theorem combined with perturbation arguments that involve the singular terms.
基金supported by the Project of Science and Technology of the Educational Department of Shandong Province(J07WH01)Binzhou University (BZCYL200416)(BZXYQMG200622)(BZXYNLG200618)
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.
文摘We prove the boundedness of all solutions for the equation x＂ ＋ V＇（x） = DxG（x,t）, where V（x） is of singular potential, i.e., limx→-1 Y（x） = ∞, and G（x, t） is bounded and periodic in t. We give sufficient conditions on V（x） and G（x, t） to ensure that all solutions are bounded.
