The authors prove that a semilinear elliptic boundary value problem has five solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues. Extensive use is made of Lyapunov–Schmidt reduction arguments, the mountain pass lemma, and characterizations of the local degree of critical points.
© 1994 Society for Industrial and Applied Mathematics
Castro, Alfonso and Cossio, Jorge, "Multiple Solutions for a Semilinear Dirichlet Problem" (1994). All HMC Faculty Publications and Research. 478.