Nonlinear Steklov problems on nonsymmetric domains

Abstract

A way of formulating nonlinear Steklov problems on nonsymmetric domains as an operator equation u = μPu, where P is completely continuous, is given. Local and global existence theorems then follow from standard techniques; these results extend earlier results for symmetric domains and equations with symmetric coefficients. Some miscellaneous results are given concerning the nature of the solution branches. © 1973.