## Periodic solutions to second order differential equations of Liénard type with jumping nonlinearities.(English)Zbl 0625.34046

This paper is devoted to the existence of periodic solutions for differential systems of the form $x'=y-F(x)+E_ 1(t),\quad y'=- g(x)+E_ 2(t)$ under the assumption that the limits $$F_ 1=\lim_{x\to -\infty}-F(x)/x,$$ $$F_ 2=\lim_{x\to +\infty}F(x)/x,$$ $$g_ 1=\lim_{x\to -\infty}g(x)/x,$$ $$g_ 2=\lim_{x\to +\infty}g(x)/x$$ exist and are finite. The proof is based upon a study of an associated homogeneous system $$x'=y-F_ 1x^--F_ 2x^+$$, $$y'=g_ 1x^--g_ 2x^+$$ and coincidence degree arguments.
Reviewer: J.Mawhin

### MSC:

 34C25 Periodic solutions to ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations
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