Nonlinear second order elliptic partial differential equations at resonance
Rita Iannacci, M. N. Nkashama, James Ward · Transactions of the American Mathematical Society · 1989
In this paper we study the solvability of boundary value problems for semilinear second order elliptic partial differential equations of resonance type in which the nonlinear perturbation is not (necessarily) required to satisfy the Landesman-Lazer condition or the monotonicity assumption. The nonlinearity may be unbounded and some crossing of eigenvalues is allowed. Selfadjoint and nonselfadjoint resonance problems are considered.