[Author]
 Bystrov, Danil V.

[Title]
 The Neumann boundary condition for a quasilinear problem with critical growth
 of the right-hand side in Lipschitz domains on a manifold

[AMS Subj-class]
 35J92 Quasilinear elliptic equations with $p$-Laplacian

[Keywords]
 quasilinear equations on manifolds, the Neumann problem, critical exponent,
 $p$-Laplacian, Lipschitz domains, convex domains

[Abstract]
 We consider the Neumann problem in the domain on manifold for an equation
 driven by $p$-Laplacian with a critical right-hand side. We give some sharp
 sufficient conditions for the existence of the least energy solution,
 requiring only local convexity of the domain, and we prove the existence
 theorem for a domain in the sphere. Similar results were previously known
 for regions with smooth or empty boundaries.

[Comments]
 Russian, 17 pp.

[Contact e-mail]
 danil.bystrovv@gmail.com