Periodic solutions for a differential inclusion problem involving the \(p(t)\)-Laplacian
The paper studies the periodic problem \[ -(|u'(t)|^{p(t)-2}u'(t))'\in \partial j(t,u(t))\quad a.e.\; t\in [0,T],\quad u(0)=u(T),\; u'(0)=u'(T), \] where \(p(.):[0,T]\to \mathbb{R}\) is continuous, \(p(t+T)=p(t)\) \(\forall t\in \mathbb{R}\), \(p(t)>1\) \(\forall t\in \mathbb{R}\), \(j(.,.):[0,T]\times {\mathbb{R}}^N\to \mathbb{R}\) is locally Lipschitz in the second variable and \(\partial j(t, .)\) denotes the subdifferential in the sense of Clarke. Under certain technical assumptions on the function \(j(.,.)\) the authors prove five results concerning the existence of a nontrivial solution of the problem considered.
scientific article; zbMATH DE number 7363135
scientific article