Existence and multiplicity of solutions for second order periodic systems with the \(p\)-Laplacian and a nonsmooth potential
The authors deals with the fractional boundary value problem for a differential inclusion \[ \begin{cases} (\|x'(t)\|^{p-2}x'(t))' \in \partial j(t,x(t))\;&\text{ a.e. } \, t\in (0,T) ,\\ x(0)=x(T),\quad x'(0)=x'(T), \end{cases}\tag{1} \] where \(1<p<+\infty,\) \(j: [0,T]\times\mathbb R^N\to\mathbb R^N\) and \(\partial j(t,\xi)\) is a subdifferential in the sense of \textit{F. H. Clarke} [Optimization and nonsmooth analysis. New York: John Wiley \& Sons (1983; Zbl 0582.49001)]. Questions of interest involve the existence and multiplicity of solutions for (1). Methods used include applications of nonsmoth second deformation lemma and nonsmooth local linking theorem.
scientific article; zbMATH DE number 5614961
scientific article