\(p\)-Laplacian and Liénard-type equation
Consider the Liénard-type equation \((*)\) \((|u'|^{p-2}u')' + \mu f(u)|u'|^{p-2}u' + g(u)=0\) where \(p>1\) and \(\mu\) is a small parameter. Under the assumptions that \(f\) and \(g\) are continuous and satisfy \(g(x)=-g(-x)\), \(g(x)x>0\) for \(x \neq 0\), \(f(x)=f(-x)\), and under additional conditions on \(F(x)=\int^x_0 f(s)ds\), the authors prove that \((*)\) has a unique limit cycle.
scientific article; zbMATH DE number 1130576