Geodesic
The Robin problem for quasilinear equations with critical growth of the right-hand side
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 51, Tome 536 (2024), pp. 126-139

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We consider the Robin problem for an equation driven by $p$-Laplacian with a critical right-hand side. For the semilinear case ($p=2$), this problem was investigated by X.-J. Wang (1991). We use a variant of the concentration-compactness method by P.-L. Lions and give some sharp sufficient conditions for the existence of the least energy solution. 
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     author = {D. V. Bystrov and A. I. Nazarov},
     title = {The {Robin} problem for quasilinear equations with critical growth of the right-hand side},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {126--139},
     publisher = {mathdoc},
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     year = {2024},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2024_536_a6/}
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D. V. Bystrov; A. I. Nazarov. The Robin problem for quasilinear equations with critical growth of the right-hand side. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 51, Tome 536 (2024), pp. 126-139. http://geodesic.mathdoc.fr/item/ZNSL_2024_536_a6/