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arXiv · 1001.5231

Existence of solutions to a higher dimensional mean-field equation on manifolds

Luca Martinazzi·Mircea Petrache
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Abstract

For $m\geq 1$ we prove an existence result for the equation $$(-Δ_g)^m u+λ=λ\frac{e^{2mu}}{\int_M e^{2mu}dμ_g}$$ on a closed Riemannian manifold $(M,g)$ of dimension $2m$ for certain values of $λ$.

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Luca Martinazzi, Mircea Petrache. 2010-01-28. Existence of solutions to a higher dimensional mean-field equation on manifolds. https://doi.org/10.1007/s00229-010-0365-1

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