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In this paper, we establish a new singular Trudinger–Moser type inequality for radial Sobolev spaces with logarithmic weights. The existence of nontrivial solutions is proved for an elliptic equation defined inℝ  n{\mathbb{R}^{n}}   , relying on variational methods and involving a nonlinearity with doubly exponential growth at infinity.

A new Singular Trudinger–Moser Type Inequality with Logarithmic Weights and Applications