Multiple solutions to asymptotically linear problems driven by superposition operators
Danilo Gregorin Afonso, Rossella Bartolo, Giovanni Molica Bisci · Journal of Mathematical Analysis and Applications · 2025
In this paper, we investigate the existence and multiplicity of weak solutions to problems involving a superposition operator of the type ∫ [ 0 , 1 ] ( − Δ ) s u d μ ( s ) , for a signed measure μ 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.