| Abstract: |
| In this talk, we deal with a class of nonlocal $(p, q)$-Kirchhoff equations in $\mathbb{R}^{N}$ involving competing nonlinearities and a critical growth term. The interplay between the nonlocal Kirchhoff coefficient and the combined action of subcritical and critical nonlinearities leads to a rich variational structure, making the analysis particularly delicate.
We focus on the existence and multiplicity of solutions, highlighting how the behavior of the system strongly depends on the interplay between the exponents and the parameter $\lambda$. In particular, we identify different regimes in which multiple solutions arise, corresponding to negative and positive energy levels, and driven by either small or large values of $\lambda$, as well as suitable conditions on the weight functions.
Our results significantly extend and refine existing results on $(p, q)$-Kirchhoff problems with critical growth.
This talk is based on a joint work with Giuseppina Autuori and Letizia Temperini. |
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