Nonlinear noncoercive Neumann problems with a reaction concave near the origin
Nonlinear noncoercive Neumann problems with a reaction concave near the origin
We consider a nonlinear Neumann problem driven by the $p$-Laplacian with a concave parametric reaction term and an asymptotically linear perturbation. We prove a multiplicity theorem producing five nontrivial solutions all with sign information when the parameter is small. For the semilinear case $(p=2)$ we produce six solutions, but we …