| Abstract: |
| In this work, we study a class of planar Kirchhoff-Choquard equations involving a sign-changing
logarithmic kernel and an exponential nonlinearity. Our main goal is to construct solutions with $k$
nodes for any given $k \in N, $ thereby establishing the multiplicity of solutions for this class of problems. To achieve this, we employ a gluing method inspired by the framework developed in [T. Bartsch, M. Willem-ARMA 1993, and, D. Cao, X. Zhu- Acta Math. Sci. 1998].
The analysis presents substantial challenges due to the interaction among the nonlocal Kirchhoff
term, the sign-changing nature of the Choquard kernel, and the lack of compactness induced by
the exponential nonlinearity, which is critical in two-dimensional settings. Overcoming these difficulties requires a careful and refined analytical approach to successfully implement the gluing
construction. |
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