Singular solutions to some non linear oblique derivative problems (Q1113005)

The purpose of this paper, which is a sequel to a previous paper by the author [Am. J. Math. 107, 591-615 (1985; Zbl 0582.35022)], is to study non-coercive oblique derivative problems obtained by combining a nonlinear elliptic second order partial differential equation with a nonlinear first order boundary condition. Using a refinement of \textit{E. Zehnder}'s generalized implicit function theorem [Commun. Pure Appl. Math. 28, 91-140 (1975; Zbl 0309.58006)], the author constructs local solutions which are not smooth up to the boundary and extends the results of the linear theory to the nonlinear case.