In this work, we study the weighted Kirchhoff problem (…) where B is the unit ball of RN , σ(x)=(log(e∣x∣))N−1 , the singular logarithm weight in the Trudinger-Moser embedding, and g is a continuous positive function on R+ . The nonlinearity is critical or subcritical growth in view of Trudinger-Moser inequalities. We first obtain the existence of a solution in the subcritical exponential growth case with positive energy by using minimax techniques combined with the Trudinger-Moser inequality. In the critical case, the associated energy does not satisfy the condition of compactness. We provide a new condition for growth, and we stress its importance to check the compactness level.
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