Superlinear convolution equations in RNRN

We give existence results for convolution equations u+κ*g(·,u)=vu+κ*g(·,u)=v on RNRN, based on degree theory for Fredholm mappings of index 0. Existence is obtained in Orlicz–Sobolev spaces W1LAW1LA adapted to the nonlinearity gg and, by a limiting process and under weaker conditions, in Lloc1. The case of R+N (Volterra equations) is also treated and applications to PDEs of the form P(D)u+Q(D)g(·,u)=fP(D)u+Q(D)g(·,u)=f are discussed.