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On a quasilinear logarithmic \(N\)-dimensional equation involving exponential growth. (English) Zbl 1501.35233

Summary: In this paper, we investigate a quasilinear logarithmic \(N\)-dimensional equation with radial potentials which can be singular at the origin, unbounded or decaying at infinity and a nonlinearity behaves like \(e^{\alpha |s|^{N / (N - 1)}}\) at infinity. The key point of our approach is a new weighted Trudinger-Moser type inequality.

MSC:

35J92 Quasilinear elliptic equations with \(p\)-Laplacian
35A01 Existence problems for PDEs: global existence, local existence, non-existence
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