| Abstract: |
| A great attention has been drawn to the study of fractional and nonlocal problems of Kirchhoff type, since they arise in a quite natural way in many different applications. The talk is based on very recent results contained in a series of papers. In particular, we present wave Kirchhoff problems driven by a nonlocal integro-differential operator and produce global existence (even under critical initial conditions), vacuum isolating and blow up of solutions. The proof arguments combine the Galerkin method with the potential well theory. The results also raise, and leave open, a number of other intriguing questions. |
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