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Singular weighted sharp Trudinger-Moser inequalities defined on $ \mathbb{R}^N $ and applications to elliptic nonlinear equations

  • *Corresponding author: Sami Aouaoui

    *Corresponding author: Sami Aouaoui 
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  • This work comes to complete some previous ones of ours. Actually, in this paper, we establish some singular weighted inequalities of Trudinger-Moser type for radial functions defined on the whole euclidean space $ \mathbb{R}^N,\ N \geq 2. $ The weights considered are of logarithmic type. The singularity plays a capital role to prove the sharpness of the inequalities. These inequalities are later improved using some concentration-compactness arguments. The last part in this work is devoted to the application of the inequalities established to some singular elliptic nonlinear equations involving a new growth conditions at infinity of exponential type.

    Mathematics Subject Classification: Primary: 26D15, 35A21, 35A23, 35B33, 35D30; Secondary: 35J20, 35J62, 35J75.


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