Periodic solutions for second order differential equations with indefinite singularities
2019 ◽
Vol 9
(1)
◽
pp. 994-1007
◽
Keyword(s):
A Priori
◽
Abstract In this paper, the problem of periodic solutions is studied for second order differential equations with indefinite singularities $$\begin{array}{} \displaystyle x''(t)+ f(x(t))x'(t)+\varphi(t)x^m(t)-\frac{\alpha(t)}{x^\mu(t)}+\frac{\beta(t)}{x^y (t)}=0, \end{array}$$ where f ∈ C((0, +∞), ℝ) may have a singularity at the origin, the signs of φ and α are allowed to change, m is a non-negative constant, μ and y are positive constants. The approach is based on a continuation theorem of Manásevich and Mawhin with techniques of a priori estimates.
2014 ◽
Vol 256
(3)
◽
pp. 895-956
◽
2009 ◽
2005 ◽
Vol 18
(11)
◽
pp. 1256-1264
◽
2006 ◽
Vol 73
(2)
◽
pp. 175-182
◽
1986 ◽
Vol 2
(1)
◽
pp. 69-77
◽
1964 ◽
Vol 65
(1)
◽
pp. 389-405
◽