This study demonstrates the existence of ground state solutions in elliptic Kirchhoff-Boussinesq problems, suggesting variational methods are effective for both subcritical and critical cases.
This paper is concerned with the existence of a ground state solution for the following class of elliptic Kirchhoff‐Boussinesq type problems given by, where with where is a bounded smooth domain in , , for and for , while is a positive function. We establish the existence of a ground state solution using variational methods. Moreover, we considered both the subcritical case, that is, , and the critical case, that is, .
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Leuyacc et al. (2025) studied this question.
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