MIN-MAX PRINCIPLES WITH NONLINEAR GENERALIZED RAYLEIGH QUOTIENTS FOR NONLINEAR EQUATIONS

摘要

We generalize the Poincaré and Courant–Fischer–Weyl min-max principles to nonlinear equations by applying the Lusternik–Schnirelmann theory to nonlinear generalized Rayleigh quotients. Based on this approach, we establish the existence of countably many solutions with prescribed energy to the Dirichlet problem with the p-Laplacian and convex-concave nonlinearity and prove new type asymptotic estimates for the spectral values of the problem.