Existence and multiplicity of positive solutions to the scalar-field equation on large annuli in the three-dimensional sphere.

Abstract: In this talk, we consider the Dirichlet problem for the scalar-field equation in a large annulus in the three-dimensional sphere. We obtain the existence, uniqueness, and multiplicity results of the positive solutions depending only on the latitude. This is joint work with Noaki Shioji (Yokohama National University) and Kohtaro Watanabe (National Defense Academy).

Posted on Oct 21, 2022 in Differential Equations, Seminars