| Abstract: |
| In this talk we will discuss the existence of groundstate solutions for certain critical Kirchhoff problems governed by a double phase operator in $\mathbb{R}^N$, involving a bounded periodic potential, a positive weight and a reaction term. Under suitable growth and monotonicity assumptions, we prove an existence result according to the size of a positive parameter $\lambda$, without the {\it Ambrosetti--Rabinowitz} condition, in the setting of Musielak--Orlicz spaces. Our proof technique relies on variational arguments including the Mountain Pass Theorem, the Nehari manifold method, concentration compactness results and the use of a suitable limiting problem.
The talk is based on a joint work with {\it Teresa Isernia}. |
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