| Abstract: |
| In this work, we study the Kirchhoff equation involving exponential non-linearity of Choquard type. We prove the existence of solution using Mountain Pass Lemma in the light of Moser, Trudinger and Adams inequalities . On the other hand, we prove the multiplicity of solution using the method of Nehari Manifold. We also study the system of Kirchhoff equation involving exponential non-linearity of Choquard type by proving new Moser, Trudinger and Adams inequalities in cartesian product of Sobolev spaces. |
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