Subharmonic bouncing solutions of generalized Lazer–Solimini equation
نویسندگان
چکیده
The paper deals with the singular differential equation x 00 + g(x) = p(t), g having a weak singularity at 0 and 2π-periodic function p. For any positive integers m n, coexistence of 2mπ-periodic bouncing solutions n impacts classical periodic solution is proven.
منابع مشابه
Subharmonic solutions of the prescribed curvature equation∗
We study the existence of subharmonic solutions of the prescribed curvature equation − ( u′/ √ 1 + u′ )′ = f(t, u). According to the behaviour at zero, or at infinity, of the prescribed curvature f , we prove the existence of arbitrarily small classical subharmonic solutions, or bounded variation subharmonic solutions with arbitrarily large oscillations. 2010 Mathematics Subject Classification:...
متن کاملExact Solutions of the Generalized Kuramoto-Sivashinsky Equation
In this paper we obtain exact solutions of the generalized Kuramoto-Sivashinsky equation, which describes manyphysical processes in motion of turbulence and other unstable process systems. The methods used to determine the exact solutions of the underlying equation are the Lie group analysis and the simplest equation method. The solutions obtained are then plotted.
متن کاملBifurcation curves of subharmonic solutions
We revisit a problem considered by Chow and Hale on the existence of subharmonic solutions for perturbed systems. In the analytic setting, under more general (weaker) conditions, we prove their results on the existence of bifurcation curves from the nonexistence to the existence of subharmonic solutions. In particular our results apply also when one has degeneracy to first order — i.e. when the...
متن کاملAnalytical Solutions to a Generalized Growth Equation
occur in the analysis of biological networks. They also include as special cases the known growth laws and probability functions, famous differential equations like those of Bessel, Chebyshev, and Laguerre, and solutions to important physical problems. These systems have no known analytical solution. However, an important subclass comprising many of the special cases mentioned above is solved. ...
متن کاملElliptic solutions to a generalized BBM equation
An approach is proposed to obtain some exact explicit solutions in terms of the Weierstrass’ elliptic function ℘ to a generalized Benjamin-Bona-Mahony (BBM) equation. Conditions for periodic and solitary wave like solutions can be expressed compactly in terms of the invariants of ℘. The approach unifies recently established ad-hoc methods to a certain extent. Evaluation of a balancing principle...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Electronic Journal of Qualitative Theory of Differential Equations
سال: 2021
ISSN: ['1417-3875']
DOI: https://doi.org/10.14232/ejqtde.2021.1.63