On a nonlinear parametric Robin problem with a locally defined reaction. (August 2019) - Gasiński, Leszek; Papageorgiou, Nikolaos S.
Abstract: We consider a nonlinear nonhomogeneous Robin problem with a parametric potential term and a Carathéodory reaction which is only locally defined. We show that for all values of the parameter in an upper half line, the equation has at least three nontrivial smooth solutions, two of constant sign and the third nodal. Under a symmetry condition on the reaction, we show the existence of a sequence of nodal solutions converging to zero in C 1 ( Ω ¯ ) .