Singular solutions to some non linear oblique derivative problems

We study some non linear and non elliptic boundary value problems obtained by considering a non linear elliptic second order partial differential equation and a non linear first order boundary condition. Relying on well-known linear results and using the Nash-Moser-type technique of a generalized implicit function theorem of Zehnder, we construct local solutions which are not smooth up to the boundary. Consequently well-known results about the non elliptic linear oblique derivative problem are extended to the non linear case. © 1988.SCOPUS: ar.j