关键词: Strong resonance, hemivariational inequality, Laplacian, principal eigenvalue, locally Lipschitz function, Clarke subdifferential, nonsmooth critical point theory

Abstract:

A semilinear elliptic equation with strong resonance at infinity and with a
nonsmooth potential is studied. Using nonsmooth critical point theory and developing some abstract minimax principles which complement and extend results in the literature, two results on existence are obtained.

Key words: Strong resonance, hemivariational inequality, Laplacian, principal eigenvalue, locally Lipschitz function, Clarke subdifferential, nonsmooth critical point theory