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In this paper we deal with the scalar curvature problem under minimal boundary mean curvature conditionon the standard 3-dimensional half-sphere. Using tools related to the theory of critical points at infinity, we give existenceresults under perturbative and nonperturbative hypothesis, and with the help of some “Morse inequalities at infinity”, we provide multiplicity results for our problem

geometry: an international journal

Existence and Multiplicity Results for the Scalar Curvature Problem on the Half-Sphere<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>𝕊</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math>

Existence and Multiplicity Results for the Scalar Curvature Problem on the Half-Sphere𝕊+3