Upper and lower bounds for higher order eigenvalues of some semilinear elliptic equations

摘要

We prove upper and lower bounds on the eigenvalues (as the H_0~1 (Ω) norm of the eigenfunction tends to zero) in bifurcation problems for a class of semilinear elliptic equations in bounded domains of R~N. It is shown that these bounds are computable in terms of the eigenvalues of the associated linear equation.