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Bifurcation results for problems with fractional Trudinger-Moser nonlinearity. (English) Zbl 1374.35185

Summary: By using a suitable topological argument based on cohomological linking and by exploiting a Trudinger-Moser inequality in fractional spaces recently obtained, we prove existence of multiple solutions for a problem involving the nonlinear fractional laplacian and a related critical exponential nonlinearity. This extends the literature for the \(N\)-Laplacian operator.

MSC:

35J92 Quasilinear elliptic equations with \(p\)-Laplacian
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
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