Landesman-Lazer conditions at half-eigenvalues of the p-Laplacian

François Genoud, Bryan P. Rynne

We study the existence of solutions of the Dirichlet problem {gather} -ϕ_p(u')' -a_+ ϕ_p(u^+) + a_- ϕ_p(u^-) -λϕ_p(u) = f(x,u), \quad x \in (0,1), \label{pb.eq} \tag{1} u(0)=u(1)=0…