The Leray-Schauder boundary condition in critical point theory
The author presents a version of Schechter's bounded mountain pass theorem in a Hilbert space not identified to its dual. An application to positive solutions of elliptic boundary value problems \[ \begin{cases} \Delta u+f(u)=0 & \text{in}\;\Omega,\\ u>0\;\text{in}\;\Omega, & u=0\;\text{on}\;\partial\Omega, \end{cases} \] is given.
scientific article; zbMATH DE number 5586853
scientific article