Periodic solutions of generalized Liénard equations
نویسندگان
چکیده
منابع مشابه
On the existence of periodic solutions for a class of generalized forced Liénard equations
In this work the second-order generalized forced Liénard equation x′′ + ( f(x)+ k(x)x′ ) x′ + g(x) = p(t) is considered and a new condition for guaranteeing the existence of at least one periodic solution for this equation is given.
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In this paper, the problem of the existence of a periodic solution is studied for the second order differential equation with a singularity of repulsive type [Formula: see text] where [Formula: see text] is singular at [Formula: see text], φ and h are T-periodic functions. By using the continuation theorem of Manásevich and Mawhin, a new result on the existence of positive periodic solution is ...
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Main Theorem. Suppose f, k, and g are real functions on R which are locally Lipschitz and p is a nonconstant, continuous, real function on [0, T ], T > 0. Also suppose all solutions of the initial value problem (1.1) can be extended to [0, T ]. If there exist real numbers a1 and a2 for which g(a1) ≤ p(t) ≤ g(a2) holds for each 0 ≤ t ≤ T , then there exists T0, 0 < T0 < T , such that if p is T0-...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1990
ISSN: 0022-247X
DOI: 10.1016/0022-247x(90)90023-9