Multiple solutions to asymptotically linear problems driven by superposition operators

Abstract

In this paper, we investigate the existence and multiplicity of weak solutions to problems involving a superposition operator of the type $${\int }_{[0,1]}(-\hat{I}”{)}^{s}ud\hat{I}¼(s),$$ for a signed measure $\hat{I}¼$ on the interval of fractional exponents $[0,1]$, when the nonlinearity is subcritical and asymptotically linear at infinity; thus, we deal with a perturbation of the eigenvalue problem for the superposition operator. We use variational tools, extending to this setting well-known results for the classical and the fractional Laplace operators.

12 pages. All comments are welcome. In this second version, we have corrected and clarified some points in the preliminaries