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 H01(Ω) norm of the eigenfunction tends to zero) in bifurcation problems for a class of semilinear elliptic equations in bounded domains of RN. It is shown that these bounds are computable in terms of the eigenvalues of the associated linear equation.