Existence and multiplicity results for nonlinear elliptic problems with linear part at resonance the case of the simple eigenvalue

AbstractWe prove existence and multiplicity theorems for nonlinear elliptic boundary value problems with noninvertible linear parts. It is considered the case in which the kernel of the linear part is unidimensional and the nonlinearity is taken either bounded or sublinear at infinity. Applications to nonlinear elasticity are given