In previous work by Castro, Cossio, and Neuberger , it was shown that a superlinear Dirichlet problem has at least three nontrivial solutions when the derivative of the nonlinearity at zero is less than the first eigenvalue of -Δ with zero Dirichlet boundry condition. One of these solutions changes sign exactly-once and the other two are of one sign. In this paper we show that when this derivative is between the k-th and k+1-st eigenvalues there still exists a solution which changes sign at most k times. In particular, when k=1 the sign-changing exactly-once solution persists although one-sign solutions no longer exist.
© 2003 Southwest Texas State University
Castro, Alfonso; Drabek, Pavel; and Neuberger, John M., "A Sign-Changing Solution for a Superlinear Dirichlet Problem, II" (2003). All HMC Faculty Publications and Research. 475.