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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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