Using Brouwer’s fixed point theorem, we prove the existence of solutions for some nonlinear problem with subcritical Sobolev exponent in S+4$S_{+}^{4}$.
In this paper, we consider the problem of prescribing the scalar curvature under minimal boundary conditions on the four dimensional half sphere. Using dynamical and topological methods involving the study of the critical points at infinity of the associated variational structure, we prove some existence results like Bahri-Coron theorem. Furthermore, we consider the approximate subcritical problem and we construct some solutions which blow up at two different points, one of them lay on the boundary and the other one is an interior point.
Berzelius failed to make use of Faraday's electrochemical laws in his laborious determination of equivalent weights.