New linking theorem and elliptic systems with nonlinear boundary condition Original Research Article

In this paper, we establish a new linking theorem without (PS)-type assumption. The new theorem produces bounded (PS) sequences. The abstract result will be used to study the existence of nontrivial (positive) solutions to the elliptic system View the MathML source with nonlinear boundary condition View the MathML source where Ω is a bounded domain of View the MathML source with smooth boundary, ∂/∂η is the outer normal derivative. We consider “weak” superlinear and asymptotically linear cases.