Multiplicity of solutions for resonant and non-resonant asymptotically linear elliptic problems

Abstract

Results about existence of a signed ground state solution and multiple solutions (if $f$ is odd with respect to the second variable) are proven for a class of asymptotically linear elliptic problems involving a Carathéodory type nonlinearity satisfying assumptions weaker than (fF) in \cite{GLZ} or $(F_2{)}_{+}$ in \cite{CM}. A close relation between the behaviour of ${\lim }_{|t|\to \infty }f(x,t)/|t|$ and the number of solutions is stablished.

arXiv comment17 pages