An existence result for a nonlinear boundary value problem via topological arguments

Khadijah Sharaf



We investigate a nonlinear PDE related to the prescribing mean curvature problem on the boundary of the unit ball. We use variational and topological methods to prove the existence of at least one solution when the function to be prescribed satisfies at its critical points a non-degeneracy condition.


Conformal metric; boundary mean curvature; lack of compactness; critical points at infinity; stable and unstable manifolds; retracts by deformation

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